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

Mar 24, 2018

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

#### Explanation:

Factoring difference of cubes (${a}^{3} - {b}^{3}$): $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

Here, $a$ is $2 x$ because the cube root of 8 is 2 and the cube root of ${x}^{3}$ is $x$, $b$ is 5 because the cube root of 125 is 5.

Plug the numbers in:

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

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

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