Question

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

Answer 1

`1000x^3-1 = (10x-1)(100x^2+10x+1)`

Explanation:

Note that both `1000x^3 = (10x)^3` and `1 = 1^3` are perfect cubes.

So we can immediately use the difference of cubes identity:

`A^3-B^3 = (A-B)(A^2+AB+B^2)`

to find:

`1000x^3-1 = (10x)^3-1^3`

`color(white)(1000x^3-1) = (10x-1)((10x)^2+10x+1)`

`color(white)(1000x^3-1) = (10x-1)(100x^2+10x+1)`