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

Question 75090: how can i factor this completely? 9x^2+12xy+4y^2-25
Found 2 solutions by checkley75, Earlsdon:
Answer by checkley75(3666) (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
--------------------------------------------------------------
X=-2Y/3+5/3 &
Y=-3X/2+5/2
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You could try this:
Try grouping the terms as follows:
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.
= Yes...a perfect square! So we can rewrite the original expression as:
Now you can see that we have the difference of two squares which can be factored thusly: Applying this to your expression, we get:

The final answer looks like:

Check: Using the FOIL method, we'll multiply the factors to see if we get the original expression back.
Simplifying this, we get: the original expression.

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