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Question 200536: a^2 b+2ab-15b=
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 
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Looking at we can see that the first term is  and the last term is  where the coefficients are 1 and -15 respectively.
Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 2? Let's list all of the factors of -15:
Factors of -15:
1,3,5,15
-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
| First Number | Second Number | Sum | | 1 | -15 | 1+(-15)=-14 | | 3 | -5 | 3+(-5)=-2 | | -1 | 15 | -1+15=14 | | -3 | 5 | -3+5=2 |
From this list we can see that -3 and 5 add up to 2 and multiply to -15
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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So our expression goes from and factors further to 
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Answer:
So completely factors to
If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.
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