SOLUTION: Please Factor the Polynomial Completely: (Is that different from factor the polynomial?) p^6-64a^6

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Question 260767: Please Factor the Polynomial Completely: (Is that different from factor the polynomial?)
p^6-64a^6
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite as
%28p%5E3%29%5E2+-+%288a%5E3%29%5E2
this is a difference of two squares, so we factor as
%28p%5E3%2B8a%5E3%29%28p%5E3-8a%5E3%29
now we can factor each parenthesis as sum and difference of cubes as
(p^3 + 8a^3) = (p+2a)(p^2-2ap+4a^2)
and
(p^3 - 8a^3) = (p-2a)(p^2+2ap+4a^2)
so our final answer is
%28p%2B2a%29%28p%5E2-2ap%2B4a%5E2%29%2A%28p-2a%29%28p%5E2%2B2ap%2B4a%5E2%29