الجبر الأمثلة

$f (x) = {(x + 4)}^{4} (x - 1) {(x + 2)}^{7}$

Step 1

بسّط وأعِد ترتيب متعدد الحدود.

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استخدِم مبرهنة ذات الحدين.

$(x^{4} + 4 x^{3} \cdot 4 + 6 x^{2} \cdot 4^{2} + 4 x \cdot 4^{3} + 4^{4}) (x - 1) {(x + 2)}^{7}$

بسّط كل حد.

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اضرب $4$ في $4$ .

$(x^{4} + 16 x^{3} + 6 x^{2} \cdot 4^{2} + 4 x \cdot 4^{3} + 4^{4}) (x - 1) {(x + 2)}^{7}$

ارفع $4$ إلى القوة $2$ .

$(x^{4} + 16 x^{3} + 6 x^{2} \cdot 16 + 4 x \cdot 4^{3} + 4^{4}) (x - 1) {(x + 2)}^{7}$

اضرب $16$ في $6$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 4 x \cdot 4^{3} + 4^{4}) (x - 1) {(x + 2)}^{7}$

اضرب $4$ في $4^{3}$ بجمع الأُسس.

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انقُل $4^{3}$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 4^{3} \cdot 4 x + 4^{4}) (x - 1) {(x + 2)}^{7}$

اضرب $4^{3}$ في $4$ .

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ارفع $4$ إلى القوة $1$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 4^{3} \cdot 4^{1} x + 4^{4}) (x - 1) {(x + 2)}^{7}$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$(x^{4} + 16 x^{3} + 96 x^{2} + 4^{3 + 1} x + 4^{4}) (x - 1) {(x + 2)}^{7}$

أضف $3$ و $1$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 4^{4} x + 4^{4}) (x - 1) {(x + 2)}^{7}$

ارفع $4$ إلى القوة $4$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 4^{4}) (x - 1) {(x + 2)}^{7}$

ارفع $4$ إلى القوة $4$ .

$(x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256) (x - 1) {(x + 2)}^{7}$

وسّع $(x^{4} + 16 x^{3} + 96 x^{2} + 256 x + 256) (x - 1)$ بضرب كل حد في العبارة الأولى في كل حد في العبارة الثانية.

$(x^{4} x + x^{4} \cdot - 1 + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

بسّط الحدود.

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بسّط كل حد.

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اضرب $x^{4}$ في $x$ بجمع الأُسس.

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اضرب $x^{4}$ في $x$ .

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ارفع $x$ إلى القوة $1$ .

$(x^{4} x^{1} + x^{4} \cdot - 1 + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$(x^{4 + 1} + x^{4} \cdot - 1 + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

أضف $4$ و $1$ .

$(x^{5} + x^{4} \cdot - 1 + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

انقُل $- 1$ إلى يسار $x^{4}$ .

$(x^{5} - 1 \cdot x^{4} + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

أعِد كتابة $- 1 x^{4}$ بالصيغة $- x^{4}$ .

$(x^{5} - x^{4} + 16 x^{3} x + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x^{3}$ في $x$ بجمع الأُسس.

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انقُل $x$ .

$(x^{5} - x^{4} + 16 (x \cdot x^{3}) + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x$ في $x^{3}$ .

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ارفع $x$ إلى القوة $1$ .

$(x^{5} - x^{4} + 16 (x^{1} x^{3}) + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$(x^{5} - x^{4} + 16 x^{1 + 3} + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

أضف $1$ و $3$ .

$(x^{5} - x^{4} + 16 x^{4} + 16 x^{3} \cdot - 1 + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $- 1$ في $16$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{2} x + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x^{2}$ في $x$ بجمع الأُسس.

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انقُل $x$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 (x \cdot x^{2}) + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x$ في $x^{2}$ .

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ارفع $x$ إلى القوة $1$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 (x^{1} x^{2}) + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{1 + 2} + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

أضف $1$ و $2$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} + 96 x^{2} \cdot - 1 + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $- 1$ في $96$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x \cdot x + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x$ في $x$ بجمع الأُسس.

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انقُل $x$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 (x \cdot x) + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $x$ في $x$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} + 256 x \cdot - 1 + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $- 1$ في $256$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} - 256 x + 256 x + 256 \cdot - 1) {(x + 2)}^{7}$

اضرب $256$ في $- 1$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} - 256 x + 256 x - 256) {(x + 2)}^{7}$

بسّط بجمع الحدود.

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جمّع الحدود المتعاكسة في $x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} - 256 x + 256 x - 256$ .

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أضف $- 256 x$ و $256 x$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} + 0 - 256) {(x + 2)}^{7}$

أضف $x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2}$ و $0$ .

$(x^{5} - x^{4} + 16 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} - 256) {(x + 2)}^{7}$

أضف $- x^{4}$ و $16 x^{4}$ .

$(x^{5} + 15 x^{4} - 16 x^{3} + 96 x^{3} - 96 x^{2} + 256 x^{2} - 256) {(x + 2)}^{7}$

أضف $- 16 x^{3}$ و $96 x^{3}$ .

$(x^{5} + 15 x^{4} + 80 x^{3} - 96 x^{2} + 256 x^{2} - 256) {(x + 2)}^{7}$

أضف $- 96 x^{2}$ و $256 x^{2}$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) {(x + 2)}^{7}$

استخدِم مبرهنة ذات الحدين.

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 7 x^{6} \cdot 2 + 21 x^{5} \cdot 2^{2} + 35 x^{4} \cdot 2^{3} + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

بسّط كل حد.

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اضرب $2$ في $7$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 21 x^{5} \cdot 2^{2} + 35 x^{4} \cdot 2^{3} + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

ارفع $2$ إلى القوة $2$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 21 x^{5} \cdot 4 + 35 x^{4} \cdot 2^{3} + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

اضرب $4$ في $21$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 35 x^{4} \cdot 2^{3} + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

ارفع $2$ إلى القوة $3$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 35 x^{4} \cdot 8 + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

اضرب $8$ في $35$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 35 x^{3} \cdot 2^{4} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

ارفع $2$ إلى القوة $4$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 35 x^{3} \cdot 16 + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

اضرب $16$ في $35$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 21 x^{2} \cdot 2^{5} + 7 x \cdot 2^{6} + 2^{7})$

ارفع $2$ إلى القوة $5$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 21 x^{2} \cdot 32 + 7 x \cdot 2^{6} + 2^{7})$

اضرب $32$ في $21$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 672 x^{2} + 7 x \cdot 2^{6} + 2^{7})$

ارفع $2$ إلى القوة $6$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 672 x^{2} + 7 x \cdot 64 + 2^{7})$

اضرب $64$ في $7$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 672 x^{2} + 448 x + 2^{7})$

ارفع $2$ إلى القوة $7$ .

$(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 672 x^{2} + 448 x + 128)$

وسّع $(x^{5} + 15 x^{4} + 80 x^{3} + 160 x^{2} - 256) (x^{7} + 14 x^{6} + 84 x^{5} + 280 x^{4} + 560 x^{3} + 672 x^{2} + 448 x + 128)$ بضرب كل حد في العبارة الأولى في كل حد في العبارة الثانية.

$x^{5} x^{7} + x^{5} (14 x^{6}) + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

بسّط الحدود.

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بسّط كل حد.

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اضرب $x^{5}$ في $x^{7}$ بجمع الأُسس.

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استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{5 + 7} + x^{5} (14 x^{6}) + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $5$ و $7$ .

$x^{12} + x^{5} (14 x^{6}) + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{5} x^{6} + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x^{6}$ بجمع الأُسس.

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انقُل $x^{6}$ .

$x^{12} + 14 (x^{6} x^{5}) + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{6 + 5} + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $6$ و $5$ .

$x^{12} + 14 x^{11} + x^{5} (84 x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{5} x^{5} + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x^{5}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{5}$ .

$x^{12} + 14 x^{11} + 84 (x^{5} x^{5}) + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{5 + 5} + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $5$ و $5$ .

$x^{12} + 14 x^{11} + 84 x^{10} + x^{5} (280 x^{4}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{5} x^{4} + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x^{4}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{4}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 (x^{4} x^{5}) + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{4 + 5} + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $4$ و $5$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + x^{5} (560 x^{3}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{5} x^{3} + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x^{3}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{3}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 (x^{3} x^{5}) + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{3 + 5} + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $3$ و $5$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + x^{5} (672 x^{2}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{5} x^{2} + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x^{2}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{2}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 (x^{2} x^{5}) + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{2 + 5} + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $2$ و $5$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + x^{5} (448 x) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{5} x + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{5}$ في $x$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 (x \cdot x^{5}) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x$ في $x^{5}$ .

انقر لعرض المزيد من الخطوات...

ارفع $x$ إلى القوة $1$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 (x^{1} x^{5}) + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{1 + 5} + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $1$ و $5$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + x^{5} \cdot 128 + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

انقُل $128$ إلى يسار $x^{5}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 \cdot x^{5} + 15 x^{4} x^{7} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{7}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{7}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 (x^{7} x^{4}) + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{7 + 4} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $7$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 15 x^{4} (14 x^{6}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 15 \cdot 14 x^{4} x^{6} + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{6}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{6}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 15 \cdot 14 (x^{6} x^{4}) + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 15 \cdot 14 x^{6 + 4} + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $6$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 15 \cdot 14 x^{10} + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $14$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 15 x^{4} (84 x^{5}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 15 \cdot 84 x^{4} x^{5} + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{5}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{5}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 15 \cdot 84 (x^{5} x^{4}) + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 15 \cdot 84 x^{5 + 4} + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $5$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 15 \cdot 84 x^{9} + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $84$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 15 x^{4} (280 x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 15 \cdot 280 x^{4} x^{4} + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{4}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{4}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 15 \cdot 280 (x^{4} x^{4}) + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 15 \cdot 280 x^{4 + 4} + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $4$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 15 \cdot 280 x^{8} + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $280$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 15 x^{4} (560 x^{3}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 15 \cdot 560 x^{4} x^{3} + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{3}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{3}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 15 \cdot 560 (x^{3} x^{4}) + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 15 \cdot 560 x^{3 + 4} + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $3$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 15 \cdot 560 x^{7} + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $560$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 15 x^{4} (672 x^{2}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 15 \cdot 672 x^{4} x^{2} + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x^{2}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{2}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 15 \cdot 672 (x^{2} x^{4}) + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 15 \cdot 672 x^{2 + 4} + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $2$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 15 \cdot 672 x^{6} + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $672$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 x^{4} (448 x) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 \cdot 448 x^{4} x + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{4}$ في $x$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 \cdot 448 (x \cdot x^{4}) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x$ في $x^{4}$ .

انقر لعرض المزيد من الخطوات...

ارفع $x$ إلى القوة $1$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 \cdot 448 (x^{1} x^{4}) + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 \cdot 448 x^{1 + 4} + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $1$ و $4$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 15 \cdot 448 x^{5} + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $15$ في $448$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 15 x^{4} \cdot 128 + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $128$ في $15$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{3} x^{7} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{7}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{7}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 (x^{7} x^{3}) + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{7 + 3} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $7$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 80 x^{3} (14 x^{6}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 80 \cdot 14 x^{3} x^{6} + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{6}$ بجمع الأُسس.

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انقُل $x^{6}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 80 \cdot 14 (x^{6} x^{3}) + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 80 \cdot 14 x^{6 + 3} + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $6$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 80 \cdot 14 x^{9} + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $14$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 80 x^{3} (84 x^{5}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 80 \cdot 84 x^{3} x^{5} + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{5}$ بجمع الأُسس.

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انقُل $x^{5}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 80 \cdot 84 (x^{5} x^{3}) + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 80 \cdot 84 x^{5 + 3} + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $5$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 80 \cdot 84 x^{8} + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $84$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 80 x^{3} (280 x^{4}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 80 \cdot 280 x^{3} x^{4} + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{4}$ بجمع الأُسس.

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انقُل $x^{4}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 80 \cdot 280 (x^{4} x^{3}) + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 80 \cdot 280 x^{4 + 3} + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $4$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 80 \cdot 280 x^{7} + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $280$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 80 x^{3} (560 x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 80 \cdot 560 x^{3} x^{3} + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{3}$ بجمع الأُسس.

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انقُل $x^{3}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 80 \cdot 560 (x^{3} x^{3}) + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 80 \cdot 560 x^{3 + 3} + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $3$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 80 \cdot 560 x^{6} + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $560$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 80 x^{3} (672 x^{2}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 80 \cdot 672 x^{3} x^{2} + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x^{2}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{2}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 80 \cdot 672 (x^{2} x^{3}) + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 80 \cdot 672 x^{2 + 3} + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $2$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 80 \cdot 672 x^{5} + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $672$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 x^{3} (448 x) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 \cdot 448 x^{3} x + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{3}$ في $x$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 \cdot 448 (x \cdot x^{3}) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x$ في $x^{3}$ .

انقر لعرض المزيد من الخطوات...

ارفع $x$ إلى القوة $1$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 \cdot 448 (x^{1} x^{3}) + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 \cdot 448 x^{1 + 3} + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $1$ و $3$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 80 \cdot 448 x^{4} + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $80$ في $448$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 80 x^{3} \cdot 128 + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $128$ في $80$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{2} x^{7} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{7}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{7}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 (x^{7} x^{2}) + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{7 + 2} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $7$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 160 x^{2} (14 x^{6}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 160 \cdot 14 x^{2} x^{6} + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{6}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{6}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 160 \cdot 14 (x^{6} x^{2}) + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 160 \cdot 14 x^{6 + 2} + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $6$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 160 \cdot 14 x^{8} + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $14$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 160 x^{2} (84 x^{5}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 160 \cdot 84 x^{2} x^{5} + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{5}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{5}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 160 \cdot 84 (x^{5} x^{2}) + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 160 \cdot 84 x^{5 + 2} + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $5$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 160 \cdot 84 x^{7} + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $84$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 160 x^{2} (280 x^{4}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 160 \cdot 280 x^{2} x^{4} + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{4}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{4}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 160 \cdot 280 (x^{4} x^{2}) + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 160 \cdot 280 x^{4 + 2} + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $4$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 160 \cdot 280 x^{6} + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $280$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 160 x^{2} (560 x^{3}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 160 \cdot 560 x^{2} x^{3} + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{3}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{3}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 160 \cdot 560 (x^{3} x^{2}) + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 160 \cdot 560 x^{3 + 2} + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $3$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 160 \cdot 560 x^{5} + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $560$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 160 x^{2} (672 x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 160 \cdot 672 x^{2} x^{2} + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x^{2}$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x^{2}$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 160 \cdot 672 (x^{2} x^{2}) + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 160 \cdot 672 x^{2 + 2} + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $2$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 160 \cdot 672 x^{4} + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $672$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 x^{2} (448 x) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 \cdot 448 x^{2} x + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x^{2}$ في $x$ بجمع الأُسس.

انقر لعرض المزيد من الخطوات...

انقُل $x$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 \cdot 448 (x \cdot x^{2}) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $x$ في $x^{2}$ .

انقر لعرض المزيد من الخطوات...

ارفع $x$ إلى القوة $1$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 \cdot 448 (x^{1} x^{2}) + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 \cdot 448 x^{1 + 2} + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

أضف $1$ و $2$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 160 \cdot 448 x^{3} + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $160$ في $448$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 160 x^{2} \cdot 128 - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $128$ في $160$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 256 (14 x^{6}) - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $14$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 256 (84 x^{5}) - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $84$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 256 (280 x^{4}) - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $280$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 256 (560 x^{3}) - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $560$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 256 (672 x^{2}) - 256 (448 x) - 256 \cdot 128$

اضرب $672$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 256 (448 x) - 256 \cdot 128$

اضرب $448$ في $- 256$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 256 \cdot 128$

اضرب $- 256$ في $128$ .

$x^{12} + 14 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 15 x^{11} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

بسّط بجمع الحدود.

انقر لعرض المزيد من الخطوات...

أضف $14 x^{11}$ و $15 x^{11}$ .

$x^{12} + 29 x^{11} + 84 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 210 x^{10} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $84 x^{10}$ و $210 x^{10}$ .

$x^{12} + 29 x^{11} + 294 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 80 x^{10} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $294 x^{10}$ و $80 x^{10}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 280 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 1260 x^{9} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $280 x^{9}$ و $1260 x^{9}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 1540 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 1120 x^{9} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $1540 x^{9}$ و $1120 x^{9}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2660 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 160 x^{9} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $2660 x^{9}$ و $160 x^{9}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 560 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 4200 x^{8} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $560 x^{8}$ و $4200 x^{8}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 4760 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 6720 x^{8} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $4760 x^{8}$ و $6720 x^{8}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 11480 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 2240 x^{8} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $11480 x^{8}$ و $2240 x^{8}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 672 x^{7} + 448 x^{6} + 128 x^{5} + 8400 x^{7} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $672 x^{7}$ و $8400 x^{7}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 9072 x^{7} + 448 x^{6} + 128 x^{5} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 22400 x^{7} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $9072 x^{7}$ و $22400 x^{7}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 31472 x^{7} + 448 x^{6} + 128 x^{5} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 13440 x^{7} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $31472 x^{7}$ و $13440 x^{7}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44912 x^{7} + 448 x^{6} + 128 x^{5} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 256 x^{7} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

اطرح $256 x^{7}$ من $44912 x^{7}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 448 x^{6} + 128 x^{5} + 10080 x^{6} + 6720 x^{5} + 1920 x^{4} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $448 x^{6}$ و $10080 x^{6}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 10528 x^{6} + 128 x^{5} + 6720 x^{5} + 1920 x^{4} + 44800 x^{6} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $10528 x^{6}$ و $44800 x^{6}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 55328 x^{6} + 128 x^{5} + 6720 x^{5} + 1920 x^{4} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 44800 x^{6} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $55328 x^{6}$ و $44800 x^{6}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 100128 x^{6} + 128 x^{5} + 6720 x^{5} + 1920 x^{4} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 3584 x^{6} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

اطرح $3584 x^{6}$ من $100128 x^{6}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128 x^{5} + 6720 x^{5} + 1920 x^{4} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $128 x^{5}$ و $6720 x^{5}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 6848 x^{5} + 1920 x^{4} + 53760 x^{5} + 35840 x^{4} + 10240 x^{3} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $6848 x^{5}$ و $53760 x^{5}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 60608 x^{5} + 1920 x^{4} + 35840 x^{4} + 10240 x^{3} + 89600 x^{5} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $60608 x^{5}$ و $89600 x^{5}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 150208 x^{5} + 1920 x^{4} + 35840 x^{4} + 10240 x^{3} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 21504 x^{5} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

اطرح $21504 x^{5}$ من $150208 x^{5}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 1920 x^{4} + 35840 x^{4} + 10240 x^{3} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $1920 x^{4}$ و $35840 x^{4}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 37760 x^{4} + 10240 x^{3} + 107520 x^{4} + 71680 x^{3} + 20480 x^{2} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $37760 x^{4}$ و $107520 x^{4}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 145280 x^{4} + 10240 x^{3} + 71680 x^{3} + 20480 x^{2} - 71680 x^{4} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

اطرح $71680 x^{4}$ من $145280 x^{4}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 73600 x^{4} + 10240 x^{3} + 71680 x^{3} + 20480 x^{2} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

أضف $10240 x^{3}$ و $71680 x^{3}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 73600 x^{4} + 81920 x^{3} + 20480 x^{2} - 143360 x^{3} - 172032 x^{2} - 114688 x - 32768$

اطرح $143360 x^{3}$ من $81920 x^{3}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 73600 x^{4} - 61440 x^{3} + 20480 x^{2} - 172032 x^{2} - 114688 x - 32768$

اطرح $172032 x^{2}$ من $20480 x^{2}$ .

$x^{12} + 29 x^{11} + 374 x^{10} + 2820 x^{9} + 13720 x^{8} + 44656 x^{7} + 96544 x^{6} + 128704 x^{5} + 73600 x^{4} - 61440 x^{3} - 151552 x^{2} - 114688 x - 32768$

Step 2

الأُس الأكبر هو درجة متعدد الحدود.

$12$