Question

How do you factor the expression `64p^3-8q^3`?

Answer 1

First, factor out the GCF, or the greatest common factor.

Explanation:

`64p^3 - 8q^3`

`=8(8p^3 - q^3)`

This can be factored as a difference of cubes `-> a^3 - b^3 = (a + b)(a + b)(a - b)`

`= 8(2p + q)(2p + q)(2p - q)`

`= 8(2p - q)(2p + q)^2`

Hopefully this helps!