document.write( "Question 141488: \"%28x%5E3-64%29%2F%288x%5E3%2B1%29\".\"%284x%5E2-1%29%2F%28x%5E2%2B4x%2B16%29\" \n" ); document.write( "
Algebra.Com's Answer #103122 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
\"%28x%5E3-64%29%2F%288x%5E3%2B1%29\".\"%284x%5E2-1%29%2F%28x%5E2%2B4x%2B16%29\"
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document.write( "Factoring rules needed:\r\n" );
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document.write( "The difference of two squares factors like this:\r\n" );
document.write( "\"FIRST%5E2-SECOND%5E2=%28FIRST-SECOND%29%28FIRST%2BSECOND%29\"\r\n" );
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document.write( "The sum of two cubes factors like this:\r\n" );
document.write( "To factor \"FIRST%5E3%2BSECOND%5E2=%28FIRST%2BSECOND%29%28FIRST%5E2-FIRST%2ASECOND%2BSECOND%5E2%29\"\r\n" );
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document.write( "The difference of two cubes factors like this:\r\n" );
document.write( "To factor \"FIRST%5E3-SECOND%5E2=%28FIRST-SECOND%29%28FIRST%5E2%2BFIRST%2ASECOND%2BSECOND%5E2%29\"\r\n" );
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document.write( "We factor \"x%5E3-64\" by writing it as \"x%5E3-4%5E3\".\r\n" );
document.write( "So it's the difference of two cubes with \"FIRST=x\" and \"SECOND=4\"\r\n" );
document.write( "So it factors as \"%28x-4%29%28x%5E2%2Bx%2A4%2B4%5E2%29=%28x-4%29%28x%5E2%2B4x%2B16%29\"\r\n" );
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document.write( "We factor \"8x%5E3%2B1\" by writing it as \"%282x%29%5E3%2B%281%29%5E3\".\r\n" );
document.write( "So it's the sum of two cubes with \"FIRST=2x\" and \"SECOND=1\"\r\n" );
document.write( "So it factors as \r\n" );
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document.write( "We factor \"4x%5E2-1\" by writing it as \"%282x%29%5E2-%281%29%5E2\".\r\n" );
document.write( "So it's the difference of two squares with \"FIRST=2x\" and \"SECOND=1\"\r\n" );
document.write( "So it factors as \"%282x-1%29%282x%2B1%29\"\r\n" );
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document.write( "So we replace everything by its factorization:\r\n" );
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document.write( "\"%28%28x-4%29%28x%5E2%2B4x%2B16%29%29%2F%28%282x%2B1%29%284x%5E2-2x%2B1%29%29\".\"%28%282x-1%29%282x%2B1%29%29%2F%28x%5E2%2B4x%2B16%29\" \r\n" );
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document.write( "We can cancel the \"%28x%5E2%2B4x%2B16%29\"'s\r\n" );
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document.write( "\"%28%28x-4%29%28cross%28x%5E2%2B4x%2B16%29%29%29%2F%28%282x%2B1%29%284x%5E2-2x%2B1%29%29\".\"%28%282x-1%29%282x%2B1%29%29%2F%28cross%28x%5E2%2B4x%2B16%29%29%29\"\r\n" );
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document.write( "And also we can cancel the \"%282x%2B1%29\"'s\r\n" );
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document.write( ".\"%28%282x-1%29cross%28%282x%2B1%29%29%29%2F%28cross%28x%5E2%2B4x%2B16%29%29%29\"\r\n" );
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document.write( "That leaves:\r\n" );
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document.write( "\"%28%28x-4%29%282x-1%29%29%2F%284x%5E2-2x%2B1%29\"\r\n" );
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document.write( "It's not necessary, but you can FOIL\r\n" );
document.write( "out the numerator and get\r\n" );
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document.write( "\"%282x%5E2-9x%2B4%29%2F%284x%5E2-2x%2B1%29\"\r\n" );
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document.write( "Edwin
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