# How do you factor 4r^2-13rt+9t^2?

May 6, 2016

$4 {r}^{2} - 13 r t + 9 {t}^{2} = \left(4 r - 9 t\right) \left(r - t\right)$

#### Explanation:

There are several ways to see this, but since the coefficients add up to $0$ we find that $\left(r - t\right)$ is a factor, which we can show by grouping:

$4 {r}^{2} - 13 r t + 9 {t}^{2}$

$= 4 {r}^{2} - 4 r t - 9 r t + 9 {t}^{2}$

$= \left(4 {r}^{2} - 4 r t\right) - \left(9 r t - 9 {t}^{2}\right)$

$= 4 r \left(r - t\right) - 9 t \left(r - t\right)$

$= \left(4 r - 9 t\right) \left(r - t\right)$