# How do you factor 24a^2 - 150b^2?

Nov 15, 2015

$24 {a}^{2} - 150 {b}^{2} = 6 \left(2 a + 5 b\right) \left(2 a - 5 b\right)$

#### Explanation:

$24 {a}^{2} - 150 {b}^{2}$

Factor out the GCF $6$.

$6 \left(4 {a}^{2} - 25 {b}^{2}\right)$

$\left(4 {a}^{2} - 25 {b}^{2}\right)$ fits the difference of squares, ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$, where $a = 2 a \mathmr{and} b = 5 b$.

$6 \left({\left(2 a\right)}^{2} - {\left(5 b\right)}^{2}\right) = 6 \left(2 a + 5 b\right) \left(2 a - 5 b\right)$