document.write( "Question 167731: Factorize\r
\n" ); document.write( "\n" ); document.write( "(x-2y)^3 + (x+2y)^3 \n" ); document.write( "

Algebra.Com's Answer #123639 by jim_thompson5910(35256) $\"\"$ $\"About$

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Let $\"w=x-2y\"$ and $\"z=x%2B2y\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the expression $\"%28x-2y%29%5E3+%2B+%28x%2B2y%29%5E3\"$ then becomes $\"w%5E3+%2B+z%5E3\"$ (through a simple substitution)\r
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\n" ); document.write( "\n" ); document.write( " $\"w%5E3%2Bz%5E3\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28w%29%5E3%2B%28z%29%5E3\"$ Rewrite $\"w%5E3\"$ as $\"%28w%29%5E3\"$ . Rewrite $\"z%5E3\"$ as $\"%28z%29%5E3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28w%2Bz%29%28%28w%29%5E2-%28w%29%28z%29%2B%28z%29%5E2%29\"$ Now factor by using the sum of cubes formula. Remember the sum of cubes formula is $\"A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28w%2Bz%29%28w%5E2-wz%2Bz%5E2%29\"$ Multiply\r
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Plug in $\"w=x-2y\"$ and $\"z=x%2B2y\"$ \r
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FOIL\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-2y%2Bx%2B2y%29%28x%5E2-4xy%2B4y%5E2-x%5E2%2B4y%5E2%2Bx%5E2%2B4xy%2B4y%5E2%29\"$ Distribute\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%28x%5E2%2B12y%5E2%29\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So $\"%28x-2y%29%5E3+%2B+%28x%2B2y%29%5E3\"$ factors to $\"2x%28x%5E2%2B12y%5E2%29\"$ .\r
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