# How do you factor 27 - x^3?

Dec 29, 2015

$27 - {x}^{3} = {3}^{3} - {x}^{3} = \left(3 - x\right) \left(9 + 3 x + {x}^{2}\right)$

#### Explanation:

$27 - {x}^{3}$ is an example of the difference of cubes, where ${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$.

Rewrite $27 - {x}^{3}$ as ${3}^{3} - {x}^{3}$, where $a = 3$ and $b = x$.

(3-x)(3^2+(3·x)+x^2)

$= \left(3 - x\right) \left(9 + 3 x + {x}^{2}\right)$