# How do you factor (3x-5)^3-125?

##### 1 Answer
Jul 18, 2016

${\left(3 x - 5\right)}^{3} - 125 = \left(3 x - 10\right) \left(9 {x}^{2} - 15 x + 25\right)$

#### Explanation:

To factorize ${\left(3 x - 5\right)}^{3} - 125$, as it is difference of two cubes, we can use the identity ${a}^{3} - {b}^{3} = \left(a + b\right) \left({a}^{2} + a b + {b}^{2}\right)$. Hence,

${\left(3 x - 5\right)}^{3} - 125$

= (3x-5-5)((3x-5)^2+5(3x-5)+5^2

= $\left(3 x - 10\right) \left(9 {x}^{2} - 30 x + 25 + 15 x - 25 + 25\right)$

= $\left(3 x - 10\right) \left(9 {x}^{2} - 15 x + 25\right)$