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

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

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

expand

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

e^{2 t} - 2 + e^{- 2 t}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(e^{t})^{2} - 2 e^{t} e^{- t} + (e^{- t})^{2} : e^{2 t} - 2 + e^{- 2 t}

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

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