document.write( "Question 236686: please help me asap\r
\n" ); document.write( "\n" ); document.write( "9x^2-35xy-4y^2\r
\n" ); document.write( "\n" ); document.write( "2x^2-xy+10xy-5y^2\r
\n" ); document.write( "\n" ); document.write( "64m^3+125n^3\r
\n" ); document.write( "\n" ); document.write( "250x^6+16y^3\r
\n" ); document.write( "\n" ); document.write( "please help me with these math problems above \n" ); document.write( "

Algebra.Com's Answer #174156 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll help you with the first two to get you going.\r
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\n" ); document.write( "\n" ); document.write( "# 1\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"9x%5E2-35xy-4y%5E2\"$ we can see that the first term is $\"9x%5E2\"$ and the last term is $\"-4y%5E2\"$ where the coefficients are 9 and -4 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 9 and the last coefficient -4 to get -36. Now what two numbers multiply to -36 and add to the middle coefficient -35? Let's list all of the factors of -36:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -36:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-9,-12,-18 ...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 -36\r
\n" ); document.write( "\n" ); document.write( "(1)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(36)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(18)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(9)\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 -35? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -35\r
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First Number	Second Number	Sum
1	-36	1+(-36)=-35
2	-18	2+(-18)=-16
3	-12	3+(-12)=-9
4	-9	4+(-9)=-5
-1	36	-1+36=35
-2	18	-2+18=16
-3	12	-3+12=9
-4	9	-4+9=5

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 1 and -36 add up to -35 and multiply to -36\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"9x%5E2-35xy-4y%5E2\"$ , replace $\"-35xy\"$ with $\"1xy%2B-36xy\"$ (notice $\"1xy%2B-36xy\"$ adds up to $\"-35xy\"$ . So it is equivalent to $\"-35xy\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2Bhighlight%281xy%2B-36xy%29%2B-4y%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"9x%5E2%2B1xy-36xy-4y%5E2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E2%2B1xy%29%2B%28-36xy-4y%5E2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%289x%2By%29-4y%289x%2By%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-4y\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-4y%29%289x%2By%29\"$ Since we have a common term of $\"9x%2By\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2%2B1xy-36xy-4y%5E2\"$ factors to $\"%28x-4y%29%289x%2By%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"9x%5E2-35xy-4y%5E2\"$ factors to $\"%28x-4y%29%289x%2By%29\"$ (since $\"9x%5E2-35xy-4y%5E2\"$ is equivalent to $\"9x%5E2%2B1xy-36xy-4y%5E2\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2-35xy-4y%5E2\"$ completely factors to $\"%28x-4y%29%289x%2By%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"9x%5E2-35xy-4y%5E2=%28x-4y%29%289x%2By%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2-xy%2B10xy-5y%5E2\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2-xy%29%2B%2810xy-5y%5E2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x-y%29%2B5y%282x-y%29\"$ Factor out the GCF $\"x\"$ out of the first group. Factor out the GCF $\"5y\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B5y%29%282x-y%29\"$ Since we have the common term $\"2x-y\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2-xy%2B10xy-5y%5E2\"$ factors to $\"%28x%2B5y%29%282x-y%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2x%5E2-xy%2B10xy-5y%5E2=%28x%2B5y%29%282x-y%29\"$
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