# How do you factor 5a^2 + 10ab - 40b^2?

One way of doing it is in the explanation

#### Explanation:

Hence we have that

5a^2+10ab-40b^2=> 5(a^2+2ab+b^2)-45b^2=> 5(a+b)^2-(sqrt45b)^2=> (sqrt5(a+b))^2-(sqrt45*b)^2=> (sqrt5*(a+b)+sqrt45*b))*(sqrt5*(a+b)-sqrt45b)

Or noticing that $\sqrt{45} = \sqrt{9 \cdot 5} = 3 \cdot \sqrt{5}$

we get that

$5 {a}^{2} + 10 a b - 40 {b}^{2} = 5 \cdot \left(a + 4 b\right) \cdot \left(a - 2 b\right)$