Pre-Algebra Examples

$\frac{16 x^{2} + 20 x + 25}{64 x^{3} - 125}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

$\frac{16 x^{2} + 20 x + 25}{{(4 x)}^{3} - 125}$

Step 1.2

Rewrite $125$ as $5^{3}$ .

$\frac{16 x^{2} + 20 x + 25}{{(4 x)}^{3} - 5^{3}}$

Step 1.3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 4 x$ and $b = 5$ .

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) ({(4 x)}^{2} + 4 x \cdot 5 + 5^{2})}$

Step 1.4

Simplify.

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Step 1.4.1

Apply the product rule to $4 x$ .

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) (4^{2} x^{2} + 4 x \cdot 5 + 5^{2})}$

Step 1.4.2

Raise $4$ to the power of $2$ .

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) (16 x^{2} + 4 x \cdot 5 + 5^{2})}$

Step 1.4.3

Multiply $5$ by $4$ .

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) (16 x^{2} + 20 x + 5^{2})}$

Step 1.4.4

Raise $5$ to the power of $2$ .

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) (16 x^{2} + 20 x + 25)}$

Step 2

Cancel the common factor of $16 x^{2} + 20 x + 25$ .

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Step 2.1

Cancel the common factor.

$\frac{16 x^{2} + 20 x + 25}{(4 x - 5) (16 x^{2} + 20 x + 25)}$

Step 2.2

Rewrite the expression.

$\frac{1}{4 x - 5}$