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}