How do you know if #4x^2 - 20x +25# is a perfect square trinomial and how do you factor it?

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Answer 1 · 2015-06-06T11:04:33

Perfect square trinomials are of the form #a^2+-2ab+b^2 = (a+-b)^2#.

In the case of #4x^2-20x+25#, we can look at the first and last terms to notice:

#4x^2 = (2x)^2#
#25 = 5^2#

...so if it is a square trinomial, we must have #a=2x# and #b=5#.

Then #2ab = 2 * 2x * 5 = 20x# matching our middle term with a minus sign.

So:

#4x^2-20x+25 = (2x)^2-(2*(2x)*5)+5^2 = (2x-5)^2#