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Question 151212This question is from textbook Intermediate Algebra
: I am having problems factoring this trinomial. The problem is 8a^2-18ay+7y^2. I would appreciate if someone could help me.
Thanks!
This question is from textbook Intermediate Algebra
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 8 and 7 respectively.
Now multiply the first coefficient 8 and the last coefficient 7 to get 56. Now what two numbers multiply to 56 and add to the middle coefficient -18? Let's list all of the factors of 56:
Factors of 56:
1,2,4,7,8,14,28,56
-1,-2,-4,-7,-8,-14,-28,-56 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 56
1*56
2*28
4*14
7*8
(-1)*(-56)
(-2)*(-28)
(-4)*(-14)
(-7)*(-8)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -18? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -18
| First Number | Second Number | Sum | | 1 | 56 | 1+56=57 | | 2 | 28 | 2+28=30 | | 4 | 14 | 4+14=18 | | 7 | 8 | 7+8=15 | | -1 | -56 | -1+(-56)=-57 | | -2 | -28 | -2+(-28)=-30 | | -4 | -14 | -4+(-14)=-18 | | -7 | -8 | -7+(-8)=-15 |
From this list we can see that -4 and -14 add up to -18 and multiply to 56
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 )
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Answer:
So factors to
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