document.write( "Question 115729: x^2y^2+3x^2y-4x^2 \n" ); document.write( "

Algebra.Com's Answer #84205 by jim_thompson5910(35256) $\"\"$ $\"About$

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Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2y%5E2%2B3x%5E2y-4x%5E2\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28y%5E2%2B3y-4%29\"$ Factor out the GCF $\"x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"y%5E2%2B3y-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"y%5E2%2B3y-4\"$ we can see that the first term is $\"y%5E2\"$ and the last term is $\"-4\"$ where the coefficients are 1 and -4 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -4 to get -4. Now what two numbers multiply to -4 and add to the middle coefficient 3? Let's list all of the factors of -4:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -4:\r
\n" ); document.write( "\n" ); document.write( "1,2\r
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\n" ); document.write( "\n" ); document.write( "-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to -4\r
\n" ); document.write( "\n" ); document.write( "(1)*(-4)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(4)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3\r
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First Number	Second Number	Sum
1	-4	1+(-4)=-3
-1	4	-1+4=3

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -1 and 4 add up to 3 and multiply to -4\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"y%5E2%2B3y-4\"$ , replace $\"3y\"$ with $\"-1y%2B4y\"$ (notice $\"-1y%2B4y\"$ adds up to $\"3y\"$ . So it is equivalent to $\"3y\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"y%5E2%2Bhighlight%28-1y%2B4y%29%2B-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"y%5E2-1y%2B4y-4\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-1y%29%2B%284y-4%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"y%28y-1%29%2B4%28y-1%29\"$ Factor out the GCF of $\"y\"$ out of the first group. Factor out the GCF of $\"4\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28y%2B4%29%28y-1%29\"$ Since we have a common term of $\"y-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"y%5E2-1y%2B4y-4\"$ factors to $\"%28y%2B4%29%28y-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"y%5E2%2B3y-4\"$ factors to $\"%28y%2B4%29%28y-1%29\"$ (since $\"y%5E2%2B3y-4\"$ is equivalent to $\"y%5E2-1y%2B4y-4\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28y%2B4%29%28y-1%29\"$ Now reintroduce the GCF\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2y%5E2%2B3x%5E2y-4x%5E2\"$ factors to $\"x%5E2%28y%2B4%29%28y-1%29\"$ \n" ); document.write( "

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