# How do you factor completely 27x^3 + 8?

Mar 25, 2018

$\left(3 x + 2\right) \left(9 {x}^{2} - 6 x + 4\right)$

#### Explanation:

Before we start, notice this: $27 {x}^{3}$ and $8$ are both perfect cubes of $3 x$ and $2$ respectively.

$27 {x}^{3} + 8$

Now, apply sum of cubes rule: ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$,

$\left(3 x + 2\right) \left(9 {x}^{2} - 6 x + 4\right)$