Factor 1-a^3

$1 - a^{3}$

Step 1

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

$1^{3} - a^{3}$

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 $a = 1$ and $b = a$ .

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

Step 3

Simplify.

One to any power is one.

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

Multiply $a$ by $1$ .

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

Factor 1-a^3

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