SOLUTION: how can i factor this completely? 9x^2+12xy+4y^2-25

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Question 75090: how can i factor this completely? 9x^2+12xy+4y^2-25
Found 2 solutions by checkley75, Earlsdon:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
9X^2+12XY+4Y^2-25
(3X+2Y)(3X+2Y)=25 TAKING THE SQUARE ROOT OF BOTH SIDES WE GET
3X+2Y=5
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X=-2Y/3+5/3 &
Y=-3X/2+5/2

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You could try this:
9x%5E2%2B12xy%2B4y%5E2-25 Try grouping the terms as follows:
%289x%5E2%2B12xy%2B4y%5E2%29-%2825%29%29 Do you notice that, in the first group, the first and last terms are perfect squares> This suggests that this trinomial might be a perfect square. Let's try it.
9x%5E2%2B12xy%2B4y%5E2+=+%283x%2B2y%29%283x%2B2y%29 = %283x%2B2y%29%5E2 Yes...a perfect square! So we can rewrite the original expression as:
%289x%5E2%2B12xy%2B4y%5E2%29-%2825%29+=+%283x%2B2y%29%5E2-%285%29%5E2 Now you can see that we have the difference of two squares which can be factored thusly: A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Applying this to your expression, we get:
%283x%2B2y%29%5E2-%285%29%5E2+=+%28%283x%2B2y%29%2B5%29%28%283x%2B2y%29-5%29
The final answer looks like:
9x%5E2%2B12xy%2B4y%5E2-25+=+%283x%2B2y%2B5%29%283x%2B2y-5%29
Check: Using the FOIL method, we'll multiply the factors to see if we get the original expression back.
%283x%2B2y%2B5%29%283x%2B2y-5%29+=+9x%5E2%2B6xy-15x%2B6xy%2B4y%5E2-10y%2B15x%2B10y-25 Simplifying this, we get:9x%5E2%2B12xy%2B4y%5E2-25 the original expression.