# How do you factor 5a^2 + 3 ab - 8b^2?

Jun 15, 2015

$5 {a}^{2} + 3 a b - 8 {b}^{2} = \left(a - b\right) \left(5 a + 8 b\right)$

#### Explanation:

Notice that the sum of the coefficients is zero:

$5 + 3 - 8 = 0$

So $\left(a - b\right)$ is a factor.

The other factor must be $\left(5 a + 8 b\right)$ to result in the required coefficients of ${a}^{2}$ and ${b}^{2}$.