# How do you factor 8x^3 - 1000?

Apr 29, 2016

$8 \left(x - 5\right) \left({x}^{2} + 5 x + 25\right)$

#### Explanation:

The first step is to 'take out' common factor of 8

$\Rightarrow 8 {x}^{3} - 1000 = 8 \left({x}^{3} - 125\right)$

now ${x}^{3} - 125 \textcolor{b l u e}{\text{ is a difference of cubes }}$

and is factorised as follows :

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)} |}}}$

now ${x}^{3} = {\left(x\right)}^{3} \text{ and } 125 = {\left(5\right)}^{3}$

for factorising purposes: a = x and b = 5

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

$\Rightarrow 8 {x}^{3} - 1000 = 8 \left(x - 5\right) \left({x}^{2} + 5 x + 25\right)$