SOLUTION: Please help with factoring the polynomial 4a^2+4ab+b^2-9

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Question 61962: Please help with factoring the polynomial 4a^2+4ab+b^2-9
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the polynomial
This is a little tricky, notice that the first three terms are a perfect square trinomial u%5E2%2B2uv%2Bv%5E2=%28u%2Bv%29%5E2
4a%5E2%2B4ab%2Bb%5E2-9
%282a%29%5E2%2B2%282a%29%28b%29%2B%28b%29%5E2-9 See what I mean, u=2a, v=b.
%282a%2Bb%29%5E2-9 Now you have the difference of squares: u%5E2-v%5E2=%28u%2Bv%29%28u-v%29
%282a%2Bb%29%5E2-%283%29%5E2 u=2a+b, v=3
%28%282a%2Bb%29%2B3%29%28%282a%2Bb%29-3%29
highlight%28%282a%2Bb%2B3%29%282a%2Bb-3%29%29
Happy Calculating!!!