Factor z^3+1

$z^{3} + 1$

Step 1

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

$z^{3} + 1^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = z$ and $b = 1$ .

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

Step 3

Simplify.

Multiply $- 1$ by $1$ .

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

One to any power is one.

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

Factor z^3+1

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