SOLUTION: Factor the polynomials completely,Show the GCF 25x^2+36y^2 I got.. (5x+6y)(5x+6y)

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Question 78114: Factor the polynomials completely,Show the GCF
25x^2+36y^2
I got..
(5x+6y)(5x+6y)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
25x%5E2%2B36y%5E2 This is not factorable.
Your answer doesn't work and you can readily see this when you multiply the factors (using FOIL) that you obtained.
%285x%2B6y%29%285x%2B6y%29+=+25x%5E2%2B30xy%2B30xy%2B36y%5E2 Simplifying this, you get:
25x%5E2%2B60xy%2B36y%5E2
If you have studied complex numbers in your math course, then you can write the factors of the given expression as follows:
25x%5E2%2B36y%5E2+=+%285x%2B6yi%29%285x-6yi%29 where i+=+sqrt%28-1%29
Let's multiply the factors and see what we get:
%285x%2B6yi%29%285x-6yi%29+=+25x%5E2%2B30xyi-30xyi-36y%5E2%28i%5E2%29 Simplifying this, we get:25x%5E2-36y%5E2%28i%5E2%29 but, recall that i%5E2+=+-1, so...
25x%5E2-36y%5E2%28-1%29+=+25x%5E2%2B36y%5E2 Does this make sense to you?