Algebra Examples

$3 x^{3} (9 x^{5} + 12 x^{6} + 24 x^{9})$

Step 1

Apply the distributive property.

$3 x^{3} (9 x^{5}) + 3 x^{3} (12 x^{6}) + 3 x^{3} (24 x^{9})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 9 x^{3} x^{5} + 3 x^{3} (12 x^{6}) + 3 x^{3} (24 x^{9})$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 9 x^{3} x^{5} + 3 \cdot 12 x^{3} x^{6} + 3 x^{3} (24 x^{9})$

Step 2.3

Rewrite using the commutative property of multiplication.

$3 \cdot 9 x^{3} x^{5} + 3 \cdot 12 x^{3} x^{6} + 3 \cdot 24 x^{3} x^{9}$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

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Step 3.1.1

Move $x^{5}$ .

$3 \cdot 9 (x^{5} x^{3}) + 3 \cdot 12 x^{3} x^{6} + 3 \cdot 24 x^{3} x^{9}$

Step 3.1.2

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

$3 \cdot 9 x^{5 + 3} + 3 \cdot 12 x^{3} x^{6} + 3 \cdot 24 x^{3} x^{9}$

Step 3.1.3

Add $5$ and $3$ .

$3 \cdot 9 x^{8} + 3 \cdot 12 x^{3} x^{6} + 3 \cdot 24 x^{3} x^{9}$

Step 3.2

Multiply $3$ by $9$ .

$27 x^{8} + 3 \cdot 12 x^{3} x^{6} + 3 \cdot 24 x^{3} x^{9}$

Step 3.3

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

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Step 3.3.1

Move $x^{6}$ .

$27 x^{8} + 3 \cdot 12 (x^{6} x^{3}) + 3 \cdot 24 x^{3} x^{9}$

Step 3.3.2

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

$27 x^{8} + 3 \cdot 12 x^{6 + 3} + 3 \cdot 24 x^{3} x^{9}$

Step 3.3.3

Add $6$ and $3$ .

$27 x^{8} + 3 \cdot 12 x^{9} + 3 \cdot 24 x^{3} x^{9}$

Step 3.4

Multiply $3$ by $12$ .

$27 x^{8} + 36 x^{9} + 3 \cdot 24 x^{3} x^{9}$

Step 3.5

Multiply $x^{3}$ by $x^{9}$ by adding the exponents.

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Step 3.5.1

Move $x^{9}$ .

$27 x^{8} + 36 x^{9} + 3 \cdot 24 (x^{9} x^{3})$

Step 3.5.2

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

$27 x^{8} + 36 x^{9} + 3 \cdot 24 x^{9 + 3}$

Step 3.5.3

Add $9$ and $3$ .

$27 x^{8} + 36 x^{9} + 3 \cdot 24 x^{12}$

Step 3.6

Multiply $3$ by $24$ .

$27 x^{8} + 36 x^{9} + 72 x^{12}$