# How do you factor 100a^6-64b^8?

Jul 13, 2015

$100 {a}^{6} - 64 {b}^{8} = 4 \left(5 {a}^{3} - 4 {b}^{4}\right) \left(5 {a}^{3} + 4 {b}^{4}\right)$

#### Explanation:

This is a difference of squares, but first separate out the common scalar factor $4$:

$100 {a}^{6} - 64 {b}^{8}$

$= 4 \left(25 {a}^{6} - 16 {b}^{8}\right)$

$= 4 \left({\left(5 {a}^{3}\right)}^{2} - {\left(4 {b}^{4}\right)}^{2}\right)$

$= 4 \left(5 {a}^{3} - 4 {b}^{4}\right) \left(5 {a}^{3} + 4 {b}^{4}\right)$

using the difference of squares identity:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

with $A = 5 {a}^{3}$ and $B = 4 {b}^{4}$