Question

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

Answer 1

This is a perfect square trinomial:

`25u^2-20uv+4v^2 = (5u-2v)^2`

Explanation:

In general we have:

`(a+b)^2 = a^2+2ab+b^2`

Notice that `25u^2 = (5u)^2` and `4v^2 = (2v)^2` are both square

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

`(5u-2v)^2 = (5u)^2+2(5u)(-2v)+(-2v)^2 = 25u^2-20uv+4v^2`