SOLUTION: Factor: 20r^2+100rg+125g^2 So far I have 5r(4r+10g)+5g(10r+25g) now I am completely stuck as to where to go from here. Thanks!

Algebra.Com
Question 303540: Factor:
20r^2+100rg+125g^2
So far I have 5r(4r+10g)+5g(10r+25g)
now I am completely stuck as to where to go from here.
Thanks!
Found 2 solutions by jim_thompson5910, mananth:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given expression


Factor out the GCF


Now let's focus on the inner expression




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



Looking at we can see that the first term is and the last term is where the coefficients are 4 and 25 respectively.

Now multiply the first coefficient 4 and the last coefficient 25 to get 100. Now what two numbers multiply to 100 and add to the middle coefficient 20? Let's list all of the factors of 100:



Factors of 100:
1,2,4,5,10,20,25,50

-1,-2,-4,-5,-10,-20,-25,-50 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 100
1*100
2*50
4*25
5*20
10*10
(-1)*(-100)
(-2)*(-50)
(-4)*(-25)
(-5)*(-20)
(-10)*(-10)

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to 20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 20

First NumberSecond NumberSum
11001+100=101
2502+50=52
4254+25=29
5205+20=25
101010+10=20
-1-100-1+(-100)=-101
-2-50-2+(-50)=-52
-4-25-4+(-25)=-29
-5-20-5+(-20)=-25
-10-10-10+(-10)=-20





From this list we can see that 10 and 10 add up to 20 and multiply to 100


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



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




So our expression goes from and factors further to


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


Answer:

So factors to

In other words,
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
20r^2+100rg+125g^2
5(4r^2+20rg+25g^2)
5{4r^2+10rg+10rg=25g^2}
5{2r(2r+5g)+5g(2r+5g)}
5{2r+5g)^2
yOU SHOULD HAVE SEPARATED THE COMMON CO-EFFICIENTS
ANANTH
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