# How do you factor 1000x^3-1?

Jun 30, 2018

$1000 {x}^{3} - 1 = \left(10 x - 1\right) \left(100 {x}^{2} + 10 x + 1\right)$

#### Explanation:

Note that both $1000 {x}^{3} = {\left(10 x\right)}^{3}$ and $1 = {1}^{3}$ are perfect cubes.

So we can immediately use the difference of cubes identity:

${A}^{3} - {B}^{3} = \left(A - B\right) \left({A}^{2} + A B + {B}^{2}\right)$

to find:

$1000 {x}^{3} - 1 = {\left(10 x\right)}^{3} - {1}^{3}$

$\textcolor{w h i t e}{1000 {x}^{3} - 1} = \left(10 x - 1\right) \left({\left(10 x\right)}^{2} + 10 x + 1\right)$

$\textcolor{w h i t e}{1000 {x}^{3} - 1} = \left(10 x - 1\right) \left(100 {x}^{2} + 10 x + 1\right)$