What is expand (e^x-e^{-x})^3 ?

The solution to expand (e^x-e^{-x})^3 is e^{3x}-3e^x+3e^{-x}-e^{-3x}

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expand (e^x-e^{-x})^3

expand

(e^{x} - e^{- x})^{3}

e^{3 x} - 3 e^{x} + 3 e^{- x} - e^{- 3 x}

Solution steps

(e^{x} - e^{- x})^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = e^{x}, b = e^{- x}

= (e^{x})^{3} - 3 (e^{x})^{2} e^{- x} + 3 e^{x} (e^{- x})^{2} - (e^{- x})^{3}

Simplify

(e^{x})^{3} - 3 (e^{x})^{2} e^{- x} + 3 e^{x} (e^{- x})^{2} - (e^{- x})^{3} : e^{3 x} - 3 e^{x} + 3 e^{- x} - e^{- 3 x}

= e^{3 x} - 3 e^{x} + 3 e^{- x} - e^{- 3 x}

(x + \frac{1}{2}) (x - \frac{1}{2})

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What is expand (e^x-e^{-x})^3 ?
The solution to expand (e^x-e^{-x})^3 is e^{3x}-3e^x+3e^{-x}-e^{-3x}