Algebra Examples

$\frac{x^{2} + 16 x + 64}{{(x + 8)}^{3} \sqrt{x + 8}}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$\frac{x^{2} + 16 x + 8^{2}}{{(x + 8)}^{3} \sqrt{x + 8}}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 x = 2 \cdot x \cdot 8$

Step 1.3

Rewrite the polynomial.

$\frac{x^{2} + 2 \cdot x \cdot 8 + 8^{2}}{{(x + 8)}^{3} \sqrt{x + 8}}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 8$ .

$\frac{{(x + 8)}^{2}}{{(x + 8)}^{3} \sqrt{x + 8}}$

Step 2

Reduce the expression $\frac{{(x + 8)}^{2}}{{(x + 8)}^{3} \sqrt{x + 8}}$ by cancelling the common factors.

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Step 2.1

Multiply by $1$ .

$\frac{{(x + 8)}^{2} \cdot 1}{{(x + 8)}^{3} \sqrt{x + 8}}$

Step 2.2

Factor ${(x + 8)}^{2}$ out of ${(x + 8)}^{3} \sqrt{x + 8}$ .

$\frac{{(x + 8)}^{2} \cdot 1}{{(x + 8)}^{2} ((x + 8) \sqrt{x + 8})}$

Step 2.3

Cancel the common factor.

$\frac{{(x + 8)}^{2} \cdot 1}{{(x + 8)}^{2} ((x + 8) \sqrt{x + 8})}$

Step 2.4

Rewrite the expression.

$\frac{1}{(x + 8) \sqrt{x + 8}}$