document.write( "Question 463239: Factor: Factor the product of polynomial\r
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Algebra.Com's Answer #317409 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "4r²-20ry+25y²\r\n" );
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document.write( "Multiply the 4 by the 25 ignoring signs.  Get 100\r\n" );
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document.write( "Write down all the ways to have two positive integers\r\n" );
document.write( "which have product 100, starting with 100*1\r\n" );
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document.write( "100*1\r\n" );
document.write( " 50*2\r\n" );
document.write( " 25*4\r\n" );
document.write( " 20*5\r\n" );
document.write( " 10*10\r\n" );
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document.write( "Since the last sign in 4r²-20ry+25y² is +, ADD them,\r\n" );
document.write( "and place the SUM out beside that:\r\n" );
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document.write( "100*1    100+1=101\r\n" );
document.write( " 50*2     50+2=52\r\n" );
document.write( " 25*4     25+4=29\r\n" );
document.write( " 20*5     20+5=25\r\n" );
document.write( " 10*10   10+10=20\r\n" );
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document.write( "Now, again ignoring signs, we find in that list of\r\n" );
document.write( "sums the coefficient of the middle term in 4r²-20ry+25y²\r\n" );
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document.write( "So we replace the number 20 by 10+10\r\n" );
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document.write( "4r²-20ry+25y²\r\n" );
document.write( "4r²-(10+10)ry+25y²\r\n" );
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document.write( "Then we distribute to remove the parentheses:\r\n" );
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document.write( "4r²-10ry-10ry+25y²\r\n" );
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document.write( "Factor the first two terms 4r²-10ry by taking out the\r\n" );
document.write( "greatest common factor, getting 2r(2r-5y)\r\n" );
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document.write( "Factor the last two terms -10ry+25y² by taking out the\r\n" );
document.write( "greatest common factor, -5y, getting -5y(2r-5y)\r\n" );
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document.write( "So we have\r\n" );
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document.write( "2r(2r-5y)-5y(2r-5y)\r\n" );
document.write( "Notice that there is a common factor, (2r-5y)\r\n" );
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document.write( "2r(2r-5y)-5y(2r-5y)\r\n" );
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document.write( "which we can factor out leaving the 2r and the -5y to put \r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "(2r-5y)(2r-5y)\r\n" );
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document.write( "But since the two factors are the same, we can write it\r\n" );
document.write( "simply as\r\n" );
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document.write( "(2r-5y)²\r\n" );
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document.write( "Edwin
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