# How do you factor 8x^3 - 27y^3?

Jun 10, 2015

$8 {x}^{3} - 27 {y}^{3} = \left(2 x - 3 y\right) \left(4 {x}^{2} + 6 x y + 9 {y}^{2}\right)$

#### Explanation:

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

$a = 2 x$
$b = 3 y$

$8 {x}^{3} - 27 {y}^{3} = \left(2 x - 3 y\right) \left(4 {x}^{2} + 6 x y + 9 {y}^{2}\right)$