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Question 248452: I just learned this today and not sure how to do this. Please help by showing how to arrive at the arrive at the answer. I have a quiz tomorrow on it. Thank you!!
x^4-15x^2y^2-16y^4
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 1 and -16 respectively.
Now multiply the first coefficient 1 and the last coefficient -16 to get -16. Now what two numbers multiply to -16 and add to the middle coefficient -15? Let's list all of the factors of -16:
Factors of -16:
1,2,4,8
-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -16
(1)*(-16)
(2)*(-8)
(-1)*(16)
(-2)*(8)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -15? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -15
| First Number | Second Number | Sum | | 1 | -16 | 1+(-16)=-15 | | 2 | -8 | 2+(-8)=-6 | | 4 | -4 | 4+(-4)=0 | | -1 | 16 | -1+16=15 | | -2 | 8 | -2+8=6 | | -4 | 4 | -4+4=0 |
From this list we can see that 1 and -16 add up to -15 and multiply to -16
Now looking at the expression , replace  with  (notice combines 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 )
Finally, the expression  is a difference of squares which means that it factors to 
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Answer:
So completely factors to 
In other words, 
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