SOLUTION: How do you completly factor, . x^2 + 12xy + 35y^2, whats the answer?

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Question 150724: How do you completly factor, . x^2 + 12xy + 35y^2, whats the answer?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here's what you're asking.
x%5E2+%2B+12xy+%2B+35y%5E2=%28ax%2Bby%29%28cx%2Bdy%29
When you multiply out the right hand side using the FOIL method you get,
%28ax%2Bby%29%28cx%2Bdy%29=acx%5E2%2B%28ad%2Bbc%29xy%2Bbdy%5E2
You know that
1.ac=1
2.bd=35
3.ad%2Bbc=12
Your choice of numbers has to satisfy all three equations.
Let's focus on 2 and factors of 35.
Let b=5, d=7.
then 3 becomes,
3.5a%2B7c=12
If we let a=c=1, we can satisfy both 1 and 3.
x%5E2+%2B+12xy+%2B+35y%5E2=%28x%2B5y%29%28x%2B7y%29