Precalculus Examples

$h^{3} - 1331$

Step 1

Rewrite $1331$ as $11^{3}$ .

$h^{3} - 11^{3}$

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 $a = h$ and $b = 11$ .

$(h - 11) (h^{2} + h \cdot 11 + 11^{2})$

Step 3

Simplify.

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Step 3.1

Move $11$ to the left of $h$ .

$(h - 11) (h^{2} + 11 h + 11^{2})$

Step 3.2

Raise $11$ to the power of $2$ .

$(h - 11) (h^{2} + 11 h + 121)$