document.write( "Question 266963: Please help me factor (with the steps included) 4x^2 - 12xy +9y^2 \n" ); document.write( "
Algebra.Com's Answer #196040 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Multiply the coefficient 4 of the first term\r\n" );
document.write( "by the coefficient 9 of the last term, getting 36.\r\n" );
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document.write( "Write down all the ways to factor 36 into \r\n" );
document.write( "the product of two integers:\r\n" );
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document.write( "36*1=36\r\n" );
document.write( "18*2=36\r\n" );
document.write( "12*3=36\r\n" );
document.write( " 9*4=36\r\n" );
document.write( " 6*6=36\r\n" );
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document.write( "Since the sign of the last term  is +,\r\n" );
document.write( "let's add the same numbers (if the last sign\r\n" );
document.write( "were negative we would subtract them)\r\n" );
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document.write( "36*1=36, 36+1=37\r\n" );
document.write( "18*2=36, 18+3=21\r\n" );
document.write( "12*3=36, 12+3=15\r\n" );
document.write( " 9*4=36,  9+4=36\r\n" );
document.write( " 6*6=36,  6+6=12\r\n" );
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document.write( "Now look among those sums for the coefficient\r\n" );
document.write( "(in absolute value) of the middle term.  The\r\n" );
document.write( "coefficient of the middle term is -12, and\r\n" );
document.write( "there is a 12 on the bottom line of the sums\r\n" );
document.write( "above, which I colored red, so replace 12 in \r\n" );
document.write( "the middle term -12xy by the (6+6) which\r\n" );
document.write( "appears just before the 12 above:\r\n" );
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document.write( "-12xy\r\n" );
document.write( "-(6+6)xy\r\n" );
document.write( "reverse the factors so you can distribute easier:\r\n" );
document.write( "-xy(6+6)\r\n" );
document.write( "Distribute:\r\n" );
document.write( "-6xy-6xy\r\n" );
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document.write( "[Notice that you could have just skipped straight\r\n" );
document.write( "from -12xy to -6xy-6xy in just one step!  I just\r\n" );
document.write( "went through that to explain why it works]\r\n" );
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document.write( "Now replace the middle term -12xy in\r\n" );
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document.write( "by the two terms -6xy-6xy\r\n" );
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document.write( "Factor 2x out of the first two terms\r\n" );
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document.write( "Factor  out of the last two terms,\r\n" );
document.write( "remembering that when you take the\r\n" );
document.write( "negative factor  out of the positive\r\n" );
document.write( "term,  you get a negative, .\r\n" );
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document.write( "Notice that you have a common binomial factor.\r\n" );
document.write( "I will color it red in both:\r\n" );
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document.write( "Now you can take out that red binomial factor\r\n" );
document.write( "the same way as you take out factors that have only\r\n" );
document.write( "one term.  You write the red binomial factor first, \r\n" );
document.write( "and then put the two remaining black factors in a \r\n" );
document.write( "parentheses after them.\r\n" );
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document.write( "Now since those just happen to be the same binomial\r\n" );
document.write( "factor we write it as just one of them squared:\r\n" );
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document.write( "Edwin
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