Examples

$x^{3} - 1$

Step 1

Rewrite

$1$ as

$1^{3}$ .

$x^{3} - 1^{3}$

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

$b = 1$ .

$(x - 1) (x^{2} + x \cdot 1 + 1^{2})$

Step 3

Simplify.

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Step 3.1

Multiply

$x$ by

$1$ .

$(x - 1) (x^{2} + x + 1^{2})$

Step 3.2

One to any power is one.

$(x - 1) (x^{2} + x + 1)$

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