# How do you factor 5x^2 + 41xy - 36y^2?

May 20, 2015

The coefficients of ${x}^{2}$ and ${y}^{2}$ are, respectively, $5$ and $- 36$. The product $5 \left(- 36\right) = - 180$, which, can be factored as $\left(- 4\right) \left(45\right)$.

So, we can now rewrite $5 {x}^{2} + 41 x y - 36 {y}^{2}$ as

$5 {x}^{2} - 4 x y + 45 x y - 36 {y}^{2}$

Now, we can factor this by two groups:

$x \left(5 x - 4 y\right)$ and $9 y \left(5 x - 4 y\right)$

We can see that the parenthesis are shared by the two factors. It becomes clearer when we rewrite:

$x \left(5 x - 4 y\right) + 9 y \left(5 x - 4 y\right) = \left(x + 9 y\right) \left(5 x - 4 y\right)$