# How do you factor 3x^3 + 27x^2y – 24xy – 216y^2?

Mar 28, 2016

$3 {x}^{3} + 27 {x}^{2} y - 24 x y - 216 {y}^{2} = 3 \left({x}^{2} - 8 y\right) \left(x + 9 y\right)$

#### Explanation:

Separate out common scalar factor $3$, then factor by grouping:

$3 {x}^{3} + 27 {x}^{2} y - 24 x y - 216 {y}^{2}$

$= 3 \left({x}^{3} + 9 {x}^{2} y - 8 x y - 72 {y}^{2}\right)$

$= 3 \left(\left({x}^{3} + 9 {x}^{2} y\right) - \left(8 x y + 72 {y}^{2}\right)\right)$

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

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