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

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Answer 1 · 2015-10-17T15:55:04

This is a perfect square trinomial:

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

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):

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

How do you factor 25u^2-20uv+4v^225u^2-20uv+4v^2?