Factor x^3+512

$x^{3} + 512$

Step 1

Rewrite $512$ as $8^{3}$ .

$x^{3} + 8^{3}$

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 $b = 8$ .

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

Step 3

Simplify.

Multiply $8$ by $- 1$ .

$(x + 8) (x^{2} - 8 x + 8^{2})$

Raise $8$ to the power of $2$ .

$(x + 8) (x^{2} - 8 x + 64)$

Factor x^3+512

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