SOLUTION: x^16-1

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Question 16514: x^16-1
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
While you didn't say what you wanted done with this expression...in fact you didn't say anything at all, but being the mind readers that we are, I would say that you want to factor this expression! It's the difference of two squares:
%28x%5E8%29%5E2+-+1%5E2%29 and can be factored as follows:
x%5E16+-+1+=%28x%5E8+-+1%29%28x%5E8+%2B+1%29 But (x^8 - 1) is also the difference of two squares and it too can be factored.
x%5E16+-+1+=+%28x%5E4+-+1%29%28x%5E4+%2B+1%29%28x%5E8+%2B+1%29 Once again, the (x^4 - 1) is the difference of two squares and it can be factored as the others could.
x%5E16+-+1+=+%28x%5E2+-+1%29%28x+%5E2+%2B+1%29%28x%5E4+%2B+1%29%28x%5E8+%2B+1%29 and finally, the (x^2 - 1) can be factored.
x%5E16+-+1+=+%28x-+1%29%28x+%2B+1%29%28x%5E2+%2B+1%29%28x%5E4+%2B+1%29%28x%5E8+%2B+1%29 The end!
We are done, except, that is, if you want to get into complex numbers, and I assume that you'd rather not.