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

Feb 22, 2016

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

Explanation:

$64 {p}^{3} - 8 {q}^{3}$

$= 8 \left(8 {p}^{3} - {q}^{3}\right)$

This can be factored as a difference of cubes $\to {a}^{3} - {b}^{3} = \left(a + b\right) \left(a + b\right) \left(a - b\right)$

$= 8 \left(2 p + q\right) \left(2 p + q\right) \left(2 p - q\right)$

$= 8 \left(2 p - q\right) {\left(2 p + q\right)}^{2}$

Hopefully this helps!