How do you factor 25u^2-20uv+4v^2?

Oct 17, 2015

This is a perfect square trinomial:

$25 {u}^{2} - 20 u v + 4 {v}^{2} = {\left(5 u - 2 v\right)}^{2}$

Explanation:

In general we have:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Notice that $25 {u}^{2} = {\left(5 u\right)}^{2}$ and $4 {v}^{2} = {\left(2 v\right)}^{2}$ are both square

So try $a = 5$, $b = - 2 v$ (- to get the minus sign for the middle term):

${\left(5 u - 2 v\right)}^{2} = {\left(5 u\right)}^{2} + 2 \left(5 u\right) \left(- 2 v\right) + {\left(- 2 v\right)}^{2} = 25 {u}^{2} - 20 u v + 4 {v}^{2}$