Algebra Examples

${(- 3 x^{4} y)}^{2} \cdot (5 x^{2} y^{6}) - {(7 x^{5} y^{4})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$5 {(- 3 x^{4} y)}^{2} x^{2} y^{6} - {(7 x^{5} y^{4})}^{2}$

Step 1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.2.1

Apply the product rule to $- 3 x^{4} y$ .

$5 ({(- 3 x^{4})}^{2} y^{2}) x^{2} y^{6} - {(7 x^{5} y^{4})}^{2}$

Step 1.2.2

Apply the product rule to $- 3 x^{4}$ .

$5 ({(- 3)}^{2} {(x^{4})}^{2} y^{2}) x^{2} y^{6} - {(7 x^{5} y^{4})}^{2}$

Step 1.3

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 1.3.1

Move $y^{6}$ .

$5 ({(- 3)}^{2} {(x^{4})}^{2} (y^{6} y^{2})) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 ({(- 3)}^{2} {(x^{4})}^{2} y^{6 + 2}) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.3.3

Add $6$ and $2$ .

$5 ({(- 3)}^{2} {(x^{4})}^{2} y^{8}) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.4

Raise $- 3$ to the power of $2$ .

$5 (9 {(x^{4})}^{2} y^{8}) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.5

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5 (9 x^{4 \cdot 2} y^{8}) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.5.2

Multiply $4$ by $2$ .

$5 (9 x^{8} y^{8}) x^{2} - {(7 x^{5} y^{4})}^{2}$

Step 1.6

Multiply $x^{8}$ by $x^{2}$ by adding the exponents.

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Step 1.6.1

Move $x^{2}$ .

$5 (9 (x^{2} x^{8}) y^{8}) - {(7 x^{5} y^{4})}^{2}$

Step 1.6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 (9 x^{2 + 8} y^{8}) - {(7 x^{5} y^{4})}^{2}$

Step 1.6.3

Add $2$ and $8$ .

$5 (9 x^{10} y^{8}) - {(7 x^{5} y^{4})}^{2}$

Step 1.7

Multiply $9$ by $5$ .

$45 (x^{10} y^{8}) - {(7 x^{5} y^{4})}^{2}$

Step 1.8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.8.1

Apply the product rule to $7 x^{5} y^{4}$ .

$45 x^{10} y^{8} - ({(7 x^{5})}^{2} {(y^{4})}^{2})$

Step 1.8.2

Apply the product rule to $7 x^{5}$ .

$45 x^{10} y^{8} - (7^{2} {(x^{5})}^{2} {(y^{4})}^{2})$

Step 1.9

Raise $7$ to the power of $2$ .

$45 x^{10} y^{8} - (49 {(x^{5})}^{2} {(y^{4})}^{2})$

Step 1.10

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 1.10.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$45 x^{10} y^{8} - (49 x^{5 \cdot 2} {(y^{4})}^{2})$

Step 1.10.2

Multiply $5$ by $2$ .

$45 x^{10} y^{8} - (49 x^{10} {(y^{4})}^{2})$

Step 1.11

Multiply the exponents in ${(y^{4})}^{2}$ .

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Step 1.11.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$45 x^{10} y^{8} - (49 x^{10} y^{4 \cdot 2})$

Step 1.11.2

Multiply $4$ by $2$ .

$45 x^{10} y^{8} - (49 x^{10} y^{8})$

Step 1.12

Multiply $49$ by $- 1$ .

$45 x^{10} y^{8} - 49 x^{10} y^{8}$

Step 2

Subtract $49 x^{10} y^{8}$ from $45 x^{10} y^{8}$ .

$- 4 x^{10} y^{8}$