# How do you factor: y= 125x^3 - 8 ?

Jul 26, 2016

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

#### Explanation:

$y = 125 {x}^{3} - 8$
or
$y = {\left(5 x\right)}^{3} - {\left(2\right)}^{3}$

Since ${a}^{3} - {b}^{3} - \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$
above equation can be written as

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