document.write( "Question 146465: I need help with some math problems Please\r
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\n" ); document.write( "\n" ); document.write( "factor the following polynomials\r
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\n" ); document.write( "\n" ); document.write( "24x^3y -8xy^2\r
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\n" ); document.write( "\n" ); document.write( "16x^2-24xy+9y^2\r
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\n" ); document.write( "\n" ); document.write( "5r^3-5\r
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\n" ); document.write( "\n" ); document.write( "(36x^2-49y^2) Thanks alot for your help!!!!!
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Algebra.Com's Answer #107073 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first two to get you started\r
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\n" ); document.write( "\n" ); document.write( " $\"24x%5E3y-8xy%5E2\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"8xy%283x%5E2-y%29\"$ Factor out the GCF $\"8xy\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"16x%5E2-24xy%2B9y%5E2\"$ we can see that the first term is $\"16x%5E2\"$ and the last term is $\"9y%5E2\"$ where the coefficients are 16 and 9 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 16 and the last coefficient 9 to get 144. Now what two numbers multiply to 144 and add to the middle coefficient -24? Let's list all of the factors of 144:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 144:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...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 144\r
\n" ); document.write( "\n" ); document.write( "1*144\r
\n" ); document.write( "\n" ); document.write( "2*72\r
\n" ); document.write( "\n" ); document.write( "3*48\r
\n" ); document.write( "\n" ); document.write( "4*36\r
\n" ); document.write( "\n" ); document.write( "6*24\r
\n" ); document.write( "\n" ); document.write( "8*18\r
\n" ); document.write( "\n" ); document.write( "9*16\r
\n" ); document.write( "\n" ); document.write( "12*12\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-144)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-72)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-36)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(-18)\r
\n" ); document.write( "\n" ); document.write( "(-9)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-12)*(-12)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -24? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -24\r
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First Number	Second Number	Sum
1	144	1+144=145
2	72	2+72=74
3	48	3+48=51
4	36	4+36=40
6	24	6+24=30
8	18	8+18=26
9	16	9+16=25
12	12	12+12=24
-1	-144	-1+(-144)=-145
-2	-72	-2+(-72)=-74
-3	-48	-3+(-48)=-51
-4	-36	-4+(-36)=-40
-6	-24	-6+(-24)=-30
-8	-18	-8+(-18)=-26
-9	-16	-9+(-16)=-25
-12	-12	-12+(-12)=-24

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -12 and -12 add up to -24 and multiply to 144\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"16x%5E2-24xy%2B9y%5E2\"$ , replace $\"-24xy\"$ with $\"-12xy%2B-12xy\"$ (notice $\"-12xy%2B-12xy\"$ adds up to $\"-24xy\"$ . So it is equivalent to $\"-24xy\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"16x%5E2%2Bhighlight%28-12xy%2B-12xy%29%2B9y%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"16x%5E2-12xy-12xy%2B9y%5E2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2816x%5E2-12xy%29%2B%28-12xy%2B9y%5E2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%284x-3y%29-3y%284x-3y%29\"$ Factor out the GCF of $\"4x\"$ out of the first group. Factor out the GCF of $\"-3y\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x-3y%29%284x-3y%29\"$ Since we have a common term of $\"4x-3y\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"16x%5E2-12xy-12xy%2B9y%5E2\"$ factors to $\"%284x-3y%29%284x-3y%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"16x%5E2-24xy%2B9y%5E2\"$ factors to $\"%284x-3y%29%284x-3y%29\"$ (since $\"16x%5E2-24xy%2B9y%5E2\"$ is equivalent to $\"16x%5E2-12xy-12xy%2B9y%5E2\"$ )\r
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\n" ); document.write( "\n" ); document.write( "note: $\"%284x-3y%29%284x-3y%29\"$ is equivalent to $\"%284x-3y%29%5E2\"$ since the term $\"4x-3y\"$ occurs twice. So $\"16x%5E2-24xy%2B9y%5E2\"$ also factors to $\"%284x-3y%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"16x%5E2-24xy%2B9y%5E2\"$ factors to $\"%284x-3y%29%5E2\"$
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