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!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at  we can see that the first term is  and the last term is  where the coefficients are 64 and 25 respectively.
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:
Factors of 1600:
1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800
-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
These factors pair up and multiply to 1600
1*1600
2*800
4*400
5*320
8*200
10*160
16*100
20*80
25*64
32*50
40*40
(-1)*(-1600)
(-2)*(-800)
(-4)*(-400)
(-5)*(-320)
(-8)*(-200)
(-10)*(-160)
(-16)*(-100)
(-20)*(-80)
(-25)*(-64)
(-32)*(-50)
(-40)*(-40)
note: remember two negative numbers multiplied together make a positive number
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
| 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 |
From this list we can see that -40 and -40 add up to -80 and multiply to 1600
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of  out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
note: is equivalent to  since the term occurs twice. So also factors to
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Answer:
So factors to
If you need more help, email me at jim_thompson5910@hotmail.com
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Jim
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