# How do you factor 27x^3-125?

Dec 11, 2015

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

#### Explanation:

you can remember to factor difference between 2 cubes as this

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

27x^"3"−125 can be written as
$= {3}^{\text{3"x^"3" - 5^"3}}$
$= \left(3 x - 5\right) \left(9 {x}^{\text{2}} + 15 x + 25\right)$
${a}^{\text{3" + b^"3}} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$