SOLUTION: Please help me solve this problem (((X^2n+2x^n y^n+y^2n))) (((X^2n-2x^n y^n+y^2n))).I really appreciate any kind of help in solving.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this problem (((X^2n+2x^n y^n+y^2n))) (((X^2n-2x^n y^n+y^2n))).I really appreciate any kind of help in solving.      Log On


   



Question 47089: Please help me solve this problem (((X^2n+2x^n y^n+y^2n))) (((X^2n-2x^n y^n+y^2n))).I really appreciate any kind of help in solving.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!

note that x%5E%282n%29+=+%28x%5En%29%5E2
and y%5E%282n%29+=+%28y%5En%29%5E2
now say w+=+x%5En+ and z+=+y%5En+
now
%28w%5E2+%2B+2wz+%2B+z%5E2%29+%2A+%28w%5E2+-+2wz+%2B+z%5E2%29
multiplying out, I get
+w%5E4+%2B+z%5E4+-+2w%5E2+%2A+z%5E2
now transform back
w+=+x%5En+
z+=+y%5En+
x%5E%284n%29+%2B+z%5E%284n%29+-+2x%5E%282n%29%2A+y%5E%282n%29+ answer
you can do a check by saying
n = 1
x = 2
y = 3
then

%284+%2B+12+%2B+9%29%2A+%284+-+12+%2B+9%29+=+25
25+=+25
x%5E%284n%29+%2B+z%5E%284n%29+-+2x%5E%282n%29%2A+y%5E%282n%29+
16+%2B+81+-+72+=+25
25+=+25
checks OK