Question

How do you factor `27 - x^3`?

Answer 1

`27-x^3=3^3-x^3=(3-x)(9+3x+x^2)`

Explanation:

`27-x^3` is an example of the difference of cubes, where `a^3-b^3=(a-b)(a^2+ab+b^2)`.

Rewrite `27-x^3` as `3^3-x^3`, where `a=3` and `b=x`.

`(3-x)(3^2+(3·x)+x^2)`

`=(3-x)(9+3x+x^2)`