# How do you factor 15r^2-16rt+4t^2?

$15 {r}^{2} - 16 r t + 4 {t}^{2} = \left(5 r - 2 t\right) \left(3 r - 2 t\right)$

#### Explanation:

We need to know the factors of 15 and 4 that will provide a sum of 16

factors of 15=3 and 5
factors of 4 = 2 an 2

By inspection , we have the numbers 2, 2, 3 , 5
We can now use the combination of 2(3) + 2(5)=6+10=16 which is the number at the middle term.

To use these numbers in factoring the arrangement should be

$\left(5 r - 2 t\right) \left(3 r - 2 t\right) = 5 r \left(3 r\right) - 2 t \left(3 r\right) - 5 r \left(2 t\right) + 2 t \left(2 t\right)$
$= 15 {r}^{2} - 16 r t + 4 {t}^{2}$

God bless....I hope the explanation is useful.