document.write( "Question 87365: factor completely
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Algebra.Com's Answer #63292 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

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\n" ); document.write( "\n" ); document.write( "\"12x%5E3-3xy%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"3x%284x%5E2-y%5E2%29\" Factor out the GCF\r
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\n" ); document.write( "\n" ); document.write( "Now lets factor \"4x%5E2-y%5E2\" using the difference of squares\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-1y%5E2\" Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( "Let \"A%5E2=4x%5E2\" and \"B%5E2=1y%5E2\". So we get this:\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-1y%5E2=A%5E2-B%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "Since \"A%5E2=4x%5E2\", A can be solved for:\r
\n" ); document.write( "\n" ); document.write( "\"sqrt%28A%5E2%29=sqrt%284x%5E2%29\" Take the square root of both sides\r
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\n" ); document.write( "\n" ); document.write( "\"A=2x\"\r
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\n" ); document.write( "\n" ); document.write( "Since \"B%5E2=1y%5E2\", B can be solved for:\r
\n" ); document.write( "\n" ); document.write( "\"sqrt%28B%5E2%29=sqrt%281y%5E2%29\" Take the square root of both sides\r
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\n" ); document.write( "\n" ); document.write( "\"B=1y\"\r
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\n" ); document.write( "\n" ); document.write( "Since we have a difference of squares, we can factor it like this:\r
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\n" ); document.write( "\n" ); document.write( "\"A%5E2-B%5E2=%28A%2BB%29%28A-B%29\"\r
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\n" ); document.write( "\n" ); document.write( "Now replace A and B\r
\n" ); document.write( "\n" ); document.write( "\"4x%5E2-1y%5E2=%282x%2B1y%29%282x-1y%29\" Plug in \"A=2x\" and \"B=1y\"\r
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\n" ); document.write( "\n" ); document.write( "So the expression\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2-1y%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "factors to\r
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\n" ); document.write( "\n" ); document.write( "\"%282x%2B1y%29%282x-1y%29\"\r
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\n" ); document.write( "\n" ); document.write( "Notice that if you foil the factored expression, you get the original expression. This verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "So \"12x%5E3-3xy%5E2\" factors to \r
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\n" ); document.write( "\n" ); document.write( "\"3x%282x%2By%29%282x-y%29\"
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