# How do you factor the expression 27x^9 + 8y^6 ?

May 28, 2016

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

#### Explanation:

$27 {x}^{9} + 8 {y}^{6}$ is a binomial each of whose monomial is a cube. Hence we can use the identity

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

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

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

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