SOLUTION: Hello, I cannot find topic - Factoring a Perfect-Square Trinomial My problem is: 16x^2 - 40x + 25 - Okay I know that the first & third #'s need to squared. But I'm g

Question 90921This question is from textbook Elementary Algebra
: Hello,
I cannot find topic - Factoring a Perfect-Square Trinomial
My problem is:
16x^2 - 40x + 25 - Okay I know that the first & third #'s need to squared.
But I'm getting lost trying to break it down.....the examples gives:
(4x)^2 - 2(4x)(5)+ 5^2 = (4x-5)^2
I just can't seem to figure out how they got there.
Thanks for any help you can give...hope it makes sense...
Cristina
This question is from textbook Elementary Algebra

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
you can build a perfect square trinomial from scratch ... (m+n)^2 ... FOILing gives m^2+mn+mn+n^2 or m^2+2mn+n^2

in your problem, m is 4x and n is -5 ... (4x-5)^2=(4x)^2+4x(-5)+4x(-5)+(-5)^2=16x^2-20x-20x+25=16x^2-40x+25

the example doesn't have the minus sign associated with the 5, which could be causing confusion
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