SOLUTION: 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!

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

------------------------------------------------------------

Answer:
So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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