SOLUTION: i was having trouble with this problem(Factor Completely) 5a^2-2ab-7b^2

Question 112030: i was having trouble with this problem(Factor Completely)
5a^2-2ab-7b^2
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 5 and -7 respectively.

Now multiply the first coefficient 5 and the last coefficient -7 to get -35. Now what two numbers multiply to -35 and add to the middle coefficient -2? Let's list all of the factors of -35:

Factors of -35:
1,5,7,35

-1,-5,-7,-35 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -35
(1)*(-35)
(5)*(-7)
(-1)*(35)
(-5)*(7)

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	-35	1+(-35)=-34
5	-7	5+(-7)=-2
-1	35	-1+35=34
-5	7	-5+7=2

From this list we can see that 5 and -7 add up to -2 and multiply to -35

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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