document.write( "Question 888446: Factor \r
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Algebra.Com's Answer #537397 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "64x³ + 125y³\r\n" );
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document.write( "There are two ways to do this.\r\n" );
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document.write( "The cube root of 64x³ is 4x and the cube root of 125y³ is 5y\r\n" );
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document.write( "You can use long division to divide by the sum (or difference if it\r\n" );
document.write( "had been the difference of two cubes) of the two cube roots, like this, \r\n" );
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document.write( "1. Divide by the sum of the cube roots of the terms\r\n" );
document.write( "   inserting two placeholder zero middle terms 0x²y + 0xy²\r\n" );
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document.write( "        16x² - 20xy  +  25y²                              \r\n" );
document.write( "4x + 5y)64x³ +  0x²y +   0xy² + 125y³\r\n" );
document.write( "        64x³ + 80x²y\r\n" );
document.write( "              -80x²y +   0xy²\r\n" );
document.write( "              -80x²y - 100xy²\r\n" );
document.write( "                       100xy² + 125y³\r\n" );
document.write( "                       100xy² + 125y³ \r\n" );
document.write( "                                   0\r\n" );
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document.write( "And so the factorization is \r\n" );
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document.write( "16x³ + 25y³ = (4x + 5y)(64x² - 20xy + 25y²)\r\n" );
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document.write( "Or you can do as most people do -- memorize how the sum or\r\n" );
document.write( "difference of two cubes factors:\r\n" );
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document.write( "A³ ± B³ = (A ± B)(A² ∓ AB + B²)\r\n" );
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document.write( "The double sign symbols ± and the ∓ mean either use the signs \r\n" );
document.write( "on top or the signs on the bottom\r\n" );
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document.write( "A will represent the cube root of the first term and B the cube root\r\n" );
document.write( "of the second term.\r\n" );
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document.write( "Your problem\r\n" );
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document.write( "64x³ + 125y³ \r\n" );
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document.write( "The cube root of 64x³ is 4x and the cube root of 125y³ is 5y.\r\n" );
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document.write( "So we substitute 4x for A and 5y for B and ± means + and ∓ means -\r\n" );
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document.write( "So A³ ± B³ = (A ± B)(A² ∓ AB + B²) becomes:\r\n" );
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document.write( "   (4x)³ + (5y)³ = (4x + 5y)[(4x)² - (4x)(5y) + (5y)²]\r\n" );
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document.write( "     16x³ + 25y³ = (4x + 5y)(64x² - 20xy + 25y²)\r\n" );
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document.write( "Edwin
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