SOLUTION: I couldnt figure out this factoring problem 4x^2+16xy-9y^2 THANKS FOR THE HELP

Question 112032: I couldnt figure out this factoring problem
4x^2+16xy-9y^2

THANKS FOR THE HELP
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 4 and -9 respectively.

Now multiply the first coefficient 4 and the last coefficient -9 to get -36. Now what two numbers multiply to -36 and add to the middle coefficient 16? Let's list all of the factors of -36:

Factors of -36:
1,2,3,4,6,9,12,18,36

-1,-2,-3,-4,-6,-9,-12,-18,-36 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -36
(1)*(-36)
(2)*(-18)
(3)*(-12)
(4)*(-9)
(-1)*(36)
(-2)*(18)
(-3)*(12)
(-4)*(9)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16

First Number	Second Number	Sum
1	-36	1+(-36)=-35
2	-18	2+(-18)=-16
3	-12	3+(-12)=-9
4	-9	4+(-9)=-5
-1	36	-1+36=35
-2	18	-2+18=16
-3	12	-3+12=9
-4	9	-4+9=5

From this list we can see that -2 and 18 add up to 16 and multiply to -36

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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