document.write( "Question 1090424: Factor 27x³ + 8y³
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Algebra.Com's Answer #704834 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Factor 27x³ + 8y³\r\n" );
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document.write( "We must memorize the rule for factoring the sum \r\n" );
document.write( "and difference of two cubes, which is:\r\n" );
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document.write( "A³ ± B³ = (A ± B)(A² ∓ AB + B²)\r\n" );
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document.write( "Notice that whatever the sign is between the terms \r\n" );
document.write( "of the original expression is the same as the sign \r\n" );
document.write( "in the first parentheses of the factorization\r\n" );
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document.write( "But the middle term in the second parentheses of\r\n" );
document.write( "the factorization gets the opposite sign.\r\n" );
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document.write( "The last term in the second parentheses of the\r\n" );
document.write( "factorization is ALWAYS + .\r\n" );
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document.write( "We now notice that 27x³ + 8y³ can be written as\r\n" );
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document.write( "3³x³ + 2³y³ which can be written as\r\n" );
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document.write( "(3x)³ + (2y)³, the sum of two cubes.\r\n" );
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document.write( "So A = 3x and B = 2y, so the signs of\r\n" );
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document.write( "A³ ± B³ = (A ± B)(A² ∓ AB + B²)\r\n" );
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document.write( "become\r\n" );
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document.write( "A³ + B³ = (A + B)(A² - AB + B²)\r\n" );
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document.write( "which upon substituting for A and B, becomes\r\n" );
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document.write( "(3x)³ + (2y)³ = [(3x) + (2y)][(3x)² - (3x)(2y) + (2y)²] =\r\n" );
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document.write( "[3x + 2y][3²x² - 6xy + 2²y²] =\r\n" );
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document.write( "(3x + 2y)(9x² - 6xy + 4y²)\r\n" );
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document.write( "Edwin
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