Question

How do you factor completely `27x^3 + 8`?

Answer 1

`(3x+2)(9x^2-6x+4)`

Explanation:

Before we start, notice this: `27x^3` and `8` are both perfect cubes of `3x` and `2` respectively.

`27x^3+8`

Now, apply sum of cubes rule: `a^3+b^3=(a+b)(a^2-ab+b^2)`,

`(3x+2)(9x^2-6x+4)`