Algebra Examples

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 x + 16}$

Step 1

Factor $2$ out of $2 x + 16$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x) + 16}$

Step 1.2

Factor $2$ out of $16$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 x + 2 \cdot 8}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 8$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x + 8)}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x + 8)}$

Step 2.2

Rewrite the expression.

$\frac{x^{2}}{x + 8} \cdot \frac{x^{2}}{x + 8}$

Step 3

Multiply $\frac{x^{2}}{x + 8} \cdot \frac{x^{2}}{x + 8}$ .

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Step 3.1

Multiply $\frac{x^{2}}{x + 8}$ by $\frac{x^{2}}{x + 8}$ .

$\frac{x^{2} x^{2}}{(x + 8) (x + 8)}$

Step 3.2

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

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Step 3.2.1

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

$\frac{x^{2 + 2}}{(x + 8) (x + 8)}$

Step 3.2.2

Add $2$ and $2$ .

$\frac{x^{4}}{(x + 8) (x + 8)}$

Step 3.3

Raise $x + 8$ to the power of $1$ .

$\frac{x^{4}}{{(x + 8)}^{1} (x + 8)}$

Step 3.4

Raise $x + 8$ to the power of $1$ .

$\frac{x^{4}}{{(x + 8)}^{1} {(x + 8)}^{1}}$

Step 3.5

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

$\frac{x^{4}}{{(x + 8)}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{x^{4}}{{(x + 8)}^{2}}$