Precalculus Examples

$z^{3} - 216$

Step 1

Rewrite $216$ as $6^{3}$ .

$z^{3} - 6^{3}$

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 $b = 6$ .

$(z - 6) (z^{2} + z \cdot 6 + 6^{2})$

Step 3

Simplify.

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Step 3.1

Move $6$ to the left of $z$ .

$(z - 6) (z^{2} + 6 z + 6^{2})$

Step 3.2

Raise $6$ to the power of $2$ .

$(z - 6) (z^{2} + 6 z + 36)$