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

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

THANKS FOR THE HELP
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at 4x%5E2%2B16xy-9y%5E2 we can see that the first term is 4x%5E2 and the last term is -9y%5E2 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 NumberSecond NumberSum
1-361+(-36)=-35
2-182+(-18)=-16
3-123+(-12)=-9
4-94+(-9)=-5
-136-1+36=35
-218-2+18=16
-312-3+12=9
-49-4+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 4x%5E2%2B16xy-9y%5E2, replace 16xy with -2xy%2B18xy (notice -2xy%2B18xy adds up to 16xy. So it is equivalent to 16xy)

4x%5E2%2Bhighlight%28-2xy%2B18xy%29%2B-9y%5E2


Now let's factor 4x%5E2-2xy%2B18xy-9y%5E2 by grouping:


%284x%5E2-2xy%29%2B%2818xy-9y%5E2%29 Group like terms


2x%282x-y%29%2B9y%282x-y%29 Factor out the GCF of 2x out of the first group. Factor out the GCF of 9y out of the second group


%282x%2B9y%29%282x-y%29 Since we have a common term of 2x-y, we can combine like terms

So 4x%5E2-2xy%2B18xy-9y%5E2 factors to %282x%2B9y%29%282x-y%29


So this also means that 4x%5E2%2B16xy-9y%5E2 factors to %282x%2B9y%29%282x-y%29 (since 4x%5E2%2B16xy-9y%5E2 is equivalent to 4x%5E2-2xy%2B18xy-9y%5E2)