Question

Which of the following is the correct factorization of polynomial below? p^3-216q^3

Answer 1

`(p-6q)(p^2+6pq+36pq^2)`

Explanation:

`p^3-216q^3`

Rewrite
`p^3-216q^3` as
`p^3-(6q)^3`:

`p^3-216q^3`

Rewrite 216 as
`6^3`

`=p^3-6^3q^3`

Apply exponent rule:
`a^mb^m=(ab)^m`

`6^3q^3=(6q)^3`

`=p^3-(6q)^3`

`=p^3-(6q)^3`

Apply difference of cubes formula:
`x^3-y^3=(x-y)(x^2+xy+y^2)`

`p^3-(6q)^3=(p-6q)(p^2+6pq+6^2q^2)`

`=(p-6q)(p^2+6pq+6^2q^2)`

Refine.

`=(p-6q)(p^2+6pq+36q^2)`