# How do you factor 32x^3-500y^3?

Dec 30, 2015

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

#### Explanation:

First extract common factors
$\left(32 {x}^{3} - 500 {y}^{3}\right) = 4 \left(8 {x}^{3} - 125 {y}^{3}\right)$
The term in brackets is now the difference of cubes, which can be factored as a^3 – b^3 = (a – b)(a^2 + ab + b^2)
So
$32 {x}^{3} - 500 {y}^{3} = 4 \left(2 x - 5 y\right) \left(4 {x}^{2} + 10 x y + 25 {y}^{2}\right)$