SOLUTION: factor (a^(2n))-1

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Question 169991: factor (a^(2n))-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E%282n%29%29-1 Start with the given expression


%28a%5En%29%5E2-1 Rewrite a%5E%282n%29 as %28a%5En%29%5E2


%28a%5En%29%5E2-1 Rewrite 1 as %281%29%5E2


Notice we have a difference of squares A%5E2-B%5E2. In this case, A=a%5En and B=1


So to factor this difference of squares, we can use the formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29


So this means that %28a%5En%29%5E2-1=%28a%5En%2B1%29%28a%5En-1%29


So %28a%5En%29%5E2-1 factors to %28a%5En%2B1%29%28a%5En-1%29