Factor z^3-125

$z^{3} - 125$

Step 1

Rewrite $125$ as $5^{3}$ .

$z^{3} - 5^{3}$

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 $a = z$ and $b = 5$ .

$(z - 5) (z^{2} + z \cdot 5 + 5^{2})$

Step 3

Simplify.

Move $5$ to the left of $z$ .

$(z - 5) (z^{2} + 5 z + 5^{2})$

Raise $5$ to the power of $2$ .

$(z - 5) (z^{2} + 5 z + 25)$

Factor z^3-125

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