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

1 Answer
Oct 17, 2015

Answer:

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#