# How do you factor 125x^3 + 8y^3?

May 21, 2015

$125 {x}^{3} + 8 {y}^{3}$

$= {\left(5 x\right)}^{3} + {\left(2 y\right)}^{3}$

$= \left(5 x + 2 y\right) \left({\left(5 x\right)}^{2} - \left(5 x\right) \left(2 y\right) + {\left(2 y\right)}^{2}\right)$

$= \left(5 x + 2 y\right) \left(25 {x}^{2} - 10 x y + 4 {y}^{2}\right)$

using the standard factorisation:

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