Factor x^3-1

$x^{3} - 1$

Rewrite $1$ as $1^{3}$ .

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

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 $b = 1$ .

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

Simplify.

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Multiply $x$ by $1$ .

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

One to any power is one.

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

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