# How do you factor 27a^3-8?

Apr 7, 2018

$27 {a}^{3} - 8 = \textcolor{red}{\left(3 a - 2\right) \left(9 {a}^{2} + 6 a + 4\right)}$

#### Explanation:

We have a difference of cubes:

$27 {a}^{3} - 8$

$= {\left(3 a\right)}^{3} - {2}^{3}$

To factor a difference of cubes, use the formula:

${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

${\left(3 a\right)}^{3} - {2}^{3} = \textcolor{red}{\left(3 a - 2\right) \left(9 {a}^{2} + 6 a + 4\right)}$

This cannot be factored any further using rational numbers, so this is the fully factored form.