document.write( "Question 359147: Please factorise the following(Please do not use the quadratic formula)\r
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Algebra.Com's Answer #256438 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Factorise:\r\n" );
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document.write( "12x² + 17xy - 5y²\r\n" );
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document.write( "Multiply the 12 by 5, disregarding the sign, getting 60.\r\n" );
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document.write( "Write down a list of all the ways to factorise 60 using two \r\n" );
document.write( "positive integers:\r\n" );
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document.write( "60*1 = 60\r\n" );
document.write( "30*2 = 60\r\n" );
document.write( "20*3 = 60\r\n" );
document.write( "15*4 = 60\r\n" );
document.write( "12*5 = 60\r\n" );
document.write( "10*6 = 60\r\n" );
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document.write( "Now look at the sign of the last term to see whether we add or\r\n" );
document.write( "subtract those pairs of numbers.  The last term is -5y², which\r\n" );
document.write( "has a - sign, so we subtract those same pairs of numbers that\r\n" );
document.write( "we multiplied above to get 60. \r\n" );
document.write( "(when the last term has a + sign, we add, but since it has a -, we subtract):\r\n" );
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document.write( "60-1 = 59\r\n" );
document.write( "30-2 = 28\r\n" );
document.write( "20-3 = 17\r\n" );
document.write( "15-4 = 11\r\n" );
document.write( "12-5 =  7\r\n" );
document.write( "10-6 =  4\r\n" );
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document.write( "And we look down that list to find the coefficient of\r\n" );
document.write( "the middle term of 12x² + 17xy - 5y², in absolute value,\r\n" );
document.write( "which is 17 and we find it as\r\n" );
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document.write( "20-3 = 17\r\n" );
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document.write( "So we substitute (20-3) in place of 17 \r\n" );
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document.write( "12x² + 17xy - 5y²\r\n" );
document.write( "12x² + (20-3)xy - 5y²\r\n" );
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document.write( "and remove the parentheses:\r\n" );
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document.write( "12x² + 20xy - 3xy - 5y²\r\n" );
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document.write( "Next we factorise only the FIRST two terms by\r\n" );
document.write( "factorising out 4x:\r\n" );
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document.write( "4x(3x + 5y) - 3xy - 5y²\r\n" );
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document.write( "Next we factorise only the LAST two terms by\r\n" );
document.write( "factorising out -y:\r\n" );
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document.write( "4x(3x + 5y) - y(3x + 5y)\r\n" );
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document.write( "Notice that the two parentheses are the same.\r\n" );
document.write( "I'll colour them red:\r\n" );
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document.write( "4x(3x + 5y) - y(3x + 5y)\r\n" );
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document.write( "So factorise out the red factor, leaving the black terms in parentheses:\r\n" );
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document.write( "(3x + 5y)(4x - y)\r\n" );
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document.write( "Edwin
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