document.write( "Question 412024: I am trying to factor this but I can't factor it?? Can you please help this is my problem 64c^2-80cx+25x^2 is this nonfactorable? THANK YOU! \n" ); document.write( "

Algebra.Com's Answer #289466 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"64c%5E2-80cx%2B25x%5E2\"$ we can see that the first term is $\"64c%5E2\"$ and the last term is $\"25x%5E2\"$ where the coefficients are 64 and 25 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 64 and the last coefficient 25 to get 1600. Now what two numbers multiply to 1600 and add to the middle coefficient -80? Let's list all of the factors of 1600:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 1600:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-16,-20,-25,-32,-40,-50,-64,-80,-100,-160,-200,-320,-400,-800 ...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 1600\r
\n" ); document.write( "\n" ); document.write( "1*1600\r
\n" ); document.write( "\n" ); document.write( "2*800\r
\n" ); document.write( "\n" ); document.write( "4*400\r
\n" ); document.write( "\n" ); document.write( "5*320\r
\n" ); document.write( "\n" ); document.write( "8*200\r
\n" ); document.write( "\n" ); document.write( "10*160\r
\n" ); document.write( "\n" ); document.write( "16*100\r
\n" ); document.write( "\n" ); document.write( "20*80\r
\n" ); document.write( "\n" ); document.write( "25*64\r
\n" ); document.write( "\n" ); document.write( "32*50\r
\n" ); document.write( "\n" ); document.write( "40*40\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-1600)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-800)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-400)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(-320)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(-200)\r
\n" ); document.write( "\n" ); document.write( "(-10)*(-160)\r
\n" ); document.write( "\n" ); document.write( "(-16)*(-100)\r
\n" ); document.write( "\n" ); document.write( "(-20)*(-80)\r
\n" ); document.write( "\n" ); document.write( "(-25)*(-64)\r
\n" ); document.write( "\n" ); document.write( "(-32)*(-50)\r
\n" ); document.write( "\n" ); document.write( "(-40)*(-40)\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 -80? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -80\r
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First Number	Second Number	Sum
1	1600	1+1600=1601
2	800	2+800=802
4	400	4+400=404
5	320	5+320=325
8	200	8+200=208
10	160	10+160=170
16	100	16+100=116
20	80	20+80=100
25	64	25+64=89
32	50	32+50=82
40	40	40+40=80
-1	-1600	-1+(-1600)=-1601
-2	-800	-2+(-800)=-802
-4	-400	-4+(-400)=-404
-5	-320	-5+(-320)=-325
-8	-200	-8+(-200)=-208
-10	-160	-10+(-160)=-170
-16	-100	-16+(-100)=-116
-20	-80	-20+(-80)=-100
-25	-64	-25+(-64)=-89
-32	-50	-32+(-50)=-82
-40	-40	-40+(-40)=-80

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -40 and -40 add up to -80 and multiply to 1600\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"64c%5E2-80cx%2B25x%5E2\"$ , replace $\"-80cx\"$ with $\"-40cx%2B-40cx\"$ (notice $\"-40cx%2B-40cx\"$ adds up to $\"-80cx\"$ . So it is equivalent to $\"-80cx\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"64c%5E2%2Bhighlight%28-40cx%2B-40cx%29%2B25x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"64c%5E2-40cx-40cx%2B25x%5E2\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2864c%5E2-40cx%29%2B%28-40cx%2B25x%5E2%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"8c%288c-5x%29-5x%288c-5x%29\"$ Factor out the GCF of $\"8c\"$ out of the first group. Factor out the GCF of $\"-5x\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%288c-5x%29%288c-5x%29\"$ Since we have a common term of $\"8c-5x\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"64c%5E2-40cx-40cx%2B25x%5E2\"$ factors to $\"%288c-5x%29%288c-5x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"64c%5E2-80cx%2B25x%5E2\"$ factors to $\"%288c-5x%29%288c-5x%29\"$ (since $\"64c%5E2-80cx%2B25x%5E2\"$ is equivalent to $\"64c%5E2-40cx-40cx%2B25x%5E2\"$ )\r
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\n" ); document.write( "\n" ); document.write( "note: $\"%288c-5x%29%288c-5x%29\"$ is equivalent to $\"%288c-5x%29%5E2\"$ since the term $\"8c-5x\"$ occurs twice. So $\"64c%5E2-80cx%2B25x%5E2\"$ also factors to $\"%288c-5x%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"64c%5E2-80cx%2B25x%5E2\"$ factors to $\"%288c-5x%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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