Question 168027: Factor by grouping
10x^2 - 12xy + 15xy - 18y^2
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! 10x^2 - 12xy + 15xy - 18y^2
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looks like xy is a common factor so you can combine those two terms.
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10x^2 + 3xy - 18y^2
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can't see any other common factors.
looks like this will be in the form of (a1*x + c1*y) * (a2*x + c2*y)
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the c coefficient of 18 can be either +/- [ 18*1, or 9*2 or 6*3 ]
the a coefficient of 10 can be either +/- [ 10*1, or 5*2 ]
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you want to get:
c1*c2 = -18
a1*c2 + a2*c1 = 3
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looks like c1*c2 can be 6*3 = -18, where either the 6 or the 3 is minus.
looks like a1*c2 + a2*c1 = 3 can be 5*3 - 2*3 with the signs put in the right place.
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working with:
c1, c2 = 6,3
a1, a2 = 2,5
we get the following combination to work:
(5x - 6y) * (2x + 3y)
multiplying this out and it becomes:
10x^2 + 15xy -12xy - 18y^2
combining like terms this becomes
10x^2 + 3x - 18y^2
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