Basic Math Examples

$z^{3} - 1000$

Step 1

Rewrite $1000$ as $10^{3}$ .

$z^{3} - 10^{3}$

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 $b = 10$ .

$(z - 10) (z^{2} + z \cdot 10 + 10^{2})$

Step 3

Simplify.

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Step 3.1

Move $10$ to the left of $z$ .

$(z - 10) (z^{2} + 10 z + 10^{2})$

Step 3.2

Raise $10$ to the power of $2$ .

$(z - 10) (z^{2} + 10 z + 100)$