What is expand (e^x-e^{-x})^2e^x ?

The solution to expand (e^x-e^{-x})^2e^x is e^{3x}-2e^x+e^{-x}

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expand (e^x-e^{-x})^2e^x

expand

(e^{x} - e^{- x})^{2} e^{x}

e^{3 x} - 2 e^{x} + e^{- x}

Solution steps

(e^{x} - e^{- x})^{2} e^{x}

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= e^{x} e^{2 x} - 2 e^{x} + e^{x} e^{- 2 x}

Simplify

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

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

R (a)^{1 - \frac{R}{k}}

\frac{a ( 1 - r )}{r + 1}

3 (2 - i) (2 + 3 i)^{i}

1 + \frac{1}{2}

(2 y^{3} - 2 y) 3^{^{'}}

What is expand (e^x-e^{-x})^2e^x ?
The solution to expand (e^x-e^{-x})^2e^x is e^{3x}-2e^x+e^{-x}