SOLUTION: Fully Factor. 1. 3a^2-36a+36 2. 4(x-3)^2 - 9(x+4)^2 Help

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Question 60905: Fully Factor.
1. 3a^2-36a+36
2. 4(x-3)^2 - 9(x+4)^2
Help
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
3a%5E2-36a%2B36
Divide both sides by 3.
Then you get 3%28a%5E2-12a%2B12%29 which doesn't factor any more.
4%28x-3%29%5E2+-+9%28x%2B4%29%5E2
Let A = x-3 and let B = x%2B4
Then the expression is this: 4A%5E2-9B%5E2
Now, 4A%5E2+=+%282A%29%5E2 and 9B%5E2+=+%283B%29%5E2
So, the expression becomes %282A%29%5E2-%283B%29%5E2
This is a difference of two squares.
It's useful to recognize that x%5E2-y%5E2 factors to %28x%2By%29%28x-y%29
So, our expression becomes %282A%2B3B%29%282A-3B%29
Now, plug in A = x-3 and B = x%2B4 into the expression.
You get %282%28x-3%29%2B3%28x%2B4%29%29%282%28x-3%29-3%28x%2B4%29%29
Multiply things out to get %282x-6%2B3x%2B12%29%282x-6-3x-12%29
Collect like terms and you get %285x%2B6%29%28-x-18%29
It's nice to move the minus sign out of the equation.
The answer then is -%285x%2B6%29%28x%2B18%29