Algebra Examples

$x^{3} - 512$

Step 1

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

$x^{3} - 8^{3}$

Step 2

Since both terms are perfect cubes, factor using the difference 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.

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Step 3.1

Move $8$ to the left of $x$ .

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

Step 3.2

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

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