Posted by Anonymous on Monday, March 12, 2012 at 2:52pm.
using the general
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
(a^x - a^-x)^3
= a^3x - 3a^2xa^-x + 3a^xa^-2x - a^-3x
= a^3x - 3a^x + 3a^-x - a^-3x
Not sure where you want to go from here.
It would be good as it is. If you want, you can replace
3a^(-x) by 3/a^x and
-a^(-3x) by -1/a^(3x)
which may be considered more explicit.
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