# How do you factor the expression -2a^2-ab+3b^2?

Mar 24, 2016

$- \left(a - b\right) \left(2 a + 3 b\right)$

#### Explanation:

−2a^2−ab+3b^2 => Factor out -1:
$= - \left(2 {a}^{2} + a b - 3 {b}^{2}\right)$
Write the 2nd term as factors of 1st and last term i.e:
$a b = - 2 a b + 3 a b$ => We get:
$= - \left(2 {a}^{2} - 2 a b + 3 a b - 3 {b}^{2}\right)$ => Factor by grouping:
$= - \left[2 a \left(a - b\right) + 3 b \left(a - b\right)\right]$ => Finally:
$= - \left(a - b\right) \left(2 a + 3 b\right)$