Question

How do you factor `2w^3 + 54`?

Answer 1

`2(w+3)(w^2-3w+9)`

Explanation:

First, factor out a common `2`.

`=2(w^3+27)`

Notice that `(w^3+27)` is a sum of cubes, which follows the rule

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

Thus,

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