Precalculus Examples

$x^{3} - 27$

Step 1

Rewrite

$27$ as

$3^{3}$ .

$x^{3} - 3^{3}$

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

$a = x$ and

$b = 3$ .

$(x - 3) (x^{2} + x \cdot 3 + 3^{2})$

Step 3

Simplify.

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Step 3.1

Move

$3$ to the left of

$x$ .

$(x - 3) (x^{2} + 3 x + 3^{2})$

Step 3.2

Raise

$3$ to the power of

$2$ .

$(x - 3) (x^{2} + 3 x + 9)$

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