Precalculus Examples

$x^{3} + 125$

Step 1

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

$x^{3} + 5^{3}$

Step 2

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

$(x + 5) (x^{2} - x \cdot 5 + 5^{2})$

Step 3

Simplify.

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Step 3.1

Multiply $5$ by $- 1$ .

$(x + 5) (x^{2} - 5 x + 5^{2})$

Step 3.2

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

$(x + 5) (x^{2} - 5 x + 25)$

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