Algebra Examples

x^{3} - 64

$x^{3} - 64$

Step 1

Rewrite

64

$64$ as

$4^{3}$ .

$x^{3} - 4^{3}$

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

$b = 4$ .

$(x - 4) (x^{2} + x \cdot 4 + 4^{2})$

Step 3

Simplify.

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Step 3.1

Move

$4$ to the left of

$x$ .

$(x - 4) (x^{2} + 4 x + 4^{2})$

Step 3.2

Raise

$4$ to the power of

$2$ .

$(x - 4) (x^{2} + 4 x + 16)$

$x^{3} - 64$

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