SOLUTION: Factor: a^6+b^6

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Question 252895: Factor: a^6+b^6
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A special case of factoring is "sum of cubes":
+a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%28a%5E2+-+ab+%2B+b%5E2%29+
.
Your problem:
a%5E6%2Bb%5E6
can be rewritten as:
%28a%5E2%29%5E3%2B%28b%5E2%29%5E3
which is "sum of cubes" which we now factor as:
%28a%5E2%2Bb%5E2%29%28%28a%5E2%29%5E2-a%5E2b%5E2%2B%28b%5E2%29%5E2%29
%28a%5E2%2Bb%5E2%29%28a%5E4-a%5E2b%5E2%2Bb%5E4%29