Pre-Algebra Examples

$9 x^{3} (x^{5} + 9 x^{3} - 5)$

Step 1

Apply the distributive property.

$9 x^{3} x^{5} + 9 x^{3} (9 x^{3}) + 9 x^{3} \cdot - 5$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{5}$ .

$9 (x^{5} x^{3}) + 9 x^{3} (9 x^{3}) + 9 x^{3} \cdot - 5$

Step 2.1.2

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

$9 x^{5 + 3} + 9 x^{3} (9 x^{3}) + 9 x^{3} \cdot - 5$

Step 2.1.3

Add $5$ and $3$ .

$9 x^{8} + 9 x^{3} (9 x^{3}) + 9 x^{3} \cdot - 5$

Step 2.2

Rewrite using the commutative property of multiplication.

$9 x^{8} + 9 \cdot 9 x^{3} x^{3} + 9 x^{3} \cdot - 5$

Step 2.3

Multiply $- 5$ by $9$ .

$9 x^{8} + 9 \cdot 9 x^{3} x^{3} - 45 x^{3}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{3}$ .

$9 x^{8} + 9 \cdot 9 (x^{3} x^{3}) - 45 x^{3}$

Step 3.1.2

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

$9 x^{8} + 9 \cdot 9 x^{3 + 3} - 45 x^{3}$

Step 3.1.3

Add $3$ and $3$ .

$9 x^{8} + 9 \cdot 9 x^{6} - 45 x^{3}$

Step 3.2

Multiply $9$ by $9$ .

$9 x^{8} + 81 x^{6} - 45 x^{3}$