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

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

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expand (e^z+e^{-z})^2

expand

(e^{z} + e^{- z})^{2}

e^{2 z} + 2 + e^{- 2 z}

Solution steps

(e^{z} + e^{- z})^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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