SOLUTION: 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-

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

------------------------------------------------------------
Answer:
So completely factors to

In other words,

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