Posted by **Anonymous** on Monday, March 12, 2012 at 2:52pm.

Multiply and Simplify:

(a^x-a^(-x))^3

=(a^x-a^(-x))(a^x-a^(-x))(a^x-a^(-x))

=(a^x-a^(-x))(a^2x-a^0-a^0+a^(-2x))

=(a^x-a^(-x))(a^2x-2+a^(-2x))

=a^3x-2a^x+a^(-x)-a^x+2a^(-x)-a^(-3x)

=a^3x-3a^x+3a^(-x)-a^(-3x)

=???

Can you simplify down any further?

please and thank you

- Math -
**Steve**, Monday, March 12, 2012 at 3:39pm
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.

- Math -
**MathMate**, Monday, March 12, 2012 at 3:41pm
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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