document.write( "Question 168027: Factor by grouping\r
\n" ); document.write( "\n" ); document.write( "10x^2 - 12xy + 15xy - 18y^2 \n" ); document.write( "
Algebra.Com's Answer #123854 by gonzo(654)\"\" \"About 
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10x^2 - 12xy + 15xy - 18y^2
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\n" ); document.write( "looks like xy is a common factor so you can combine those two terms.
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\n" ); document.write( "10x^2 + 3xy - 18y^2
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\n" ); document.write( "can't see any other common factors.
\n" ); document.write( "looks like this will be in the form of (a1*x + c1*y) * (a2*x + c2*y)
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\n" ); document.write( "the c coefficient of 18 can be either +/- [ 18*1, or 9*2 or 6*3 ]
\n" ); document.write( "the a coefficient of 10 can be either +/- [ 10*1, or 5*2 ]
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\n" ); document.write( "you want to get:
\n" ); document.write( "c1*c2 = -18
\n" ); document.write( "a1*c2 + a2*c1 = 3
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\n" ); document.write( "looks like c1*c2 can be 6*3 = -18, where either the 6 or the 3 is minus.
\n" ); document.write( "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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\n" ); document.write( "working with:
\n" ); document.write( "c1, c2 = 6,3
\n" ); document.write( "a1, a2 = 2,5
\n" ); document.write( "we get the following combination to work:
\n" ); document.write( "(5x - 6y) * (2x + 3y)
\n" ); document.write( "multiplying this out and it becomes:
\n" ); document.write( "10x^2 + 15xy -12xy - 18y^2
\n" ); document.write( "combining like terms this becomes
\n" ); document.write( "10x^2 + 3x - 18y^2
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