document.write( "Question 490667: Hi i need help please....\r
\n" ); document.write( "\n" ); document.write( "Factor the expression 36x^2-24xy+4y^2 into a product of binomials. \n" ); document.write( "

Algebra.Com's Answer #334251 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"36x%5E2-24xy%2B4y%5E2\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"4%289x%5E2-6xy%2By%5E2%29\"$ Factor out the GCF $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"9x%5E2-6xy%2By%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"9x%5E2-6xy%2By%5E2\"$ , we can see that the first coefficient is $\"9\"$ , the second coefficient is $\"-6\"$ , and the last coefficient is $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"9\"$ by the last coefficient $\"1\"$ to get $\"%289%29%281%29=9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"9\"$ (the previous product) and add to the second coefficient $\"-6\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"9\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"9\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,9\r
\n" ); document.write( "\n" ); document.write( "-1,-3,-9\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. 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 $\"9\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*9 = 9
\n" ); document.write( "3*3 = 9
\n" ); document.write( "(-1)*(-9) = 9
\n" ); document.write( "(-3)*(-3) = 9\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-6\"$ :\r
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First Number	Second Number	Sum
1	9	1+9=10
3	3	3+3=6
-1	-9	-1+(-9)=-10
-3	-3	-3+(-3)=-6

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-3\"$ add to $\"-6\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-3\"$ both multiply to $\"9\"$ and add to $\"-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-6xy\"$ with $\"-3xy-3xy\"$ . Remember, $\"-3\"$ and $\"-3\"$ add to $\"-6\"$ . So this shows us that $\"-3xy-3xy=-6xy\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2Bhighlight%28-3xy-3xy%29%2By%5E2\"$ Replace the second term $\"-6xy\"$ with $\"-3xy-3xy\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E2-3xy%29%2B%28-3xy%2By%5E2%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%283x-y%29%2B%28-3xy%2By%5E2%29\"$ Factor out the GCF $\"3x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%283x-y%29-y%283x-y%29\"$ Factor out $\"-y\"$ from the second group.\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x-y%29%283x-y%29\"$ Factor out $\"3x-y\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%283x-y%29%5E2\"$ Condense\r
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\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2-6xy%2By%5E2\"$ factors to $\"%283x-y%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "This then means that $\"4%289x%5E2-6xy%2By%5E2%29\"$ becomes $\"4%283x-y%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the final answer is $\"4%283x-y%29%5E2\"$
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