# How do you factor 5a^2 + 10ab - 15b^2?

May 27, 2015

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

$= 5 \left(a - b\right) \left(a + 3 b\right)$

Check: y = 5(a^2 + 3ab - ab - 5b) . OK

May 27, 2015

To factor $5 {a}^{2} + 10 a b - 15 {b}^{2}$
first extract the obvious common constant factor
then look for factors of the simplified variable term

$5 {a}^{2} + 10 a b - 15 {b}^{2}$
$= 5 \left({a}^{2} + 2 a b - 3 {b}^{2}\right)$

$= 5 \left(a + 3 b\right) \left(a - b\right)$