Question

How do you factor `5w^3-1080`?

Answer 1

`5w^3-1080 = 5(w-6)(w^2+6w+36)`

Explanation:

The difference of cubes identity can be written:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

We can use this with `a=w` and `b=6` as follows:

`5w^3-1080 = 5(w^3-216)`

`color(white)(5w^3-1080) = 5(w^3-6^3)`

`color(white)(5w^3-1080) = 5(w-6)(w^2+6w+6^2)`

`color(white)(5w^3-1080) = 5(w-6)(w^2+6w+36)`

The remaining quadratic factor has no linear factors with Real coefficients.