What is expand (e^{4t}+e^{-4t})^2 ?

The solution to expand (e^{4t}+e^{-4t})^2 is e^{8t}+2+e^{-8t}

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expand (e^{4t}+e^{-4t})^2

expand

(e^{4 t} + e^{- 4 t})^{2}

e^{8 t} + 2 + e^{- 8 t}

Solution steps

(e^{4 t} + e^{- 4 t})^{2}

Apply Perfect Square Formula:

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

a = e^{4 t}, b = e^{- 4 t}

= (e^{4 t})^{2} + 2 e^{4 t} e^{- 4 t} + (e^{- 4 t})^{2}

Simplify

(e^{4 t})^{2} + 2 e^{4 t} e^{- 4 t} + (e^{- 4 t})^{2} : e^{8 t} + 2 + e^{- 8 t}

= e^{8 t} + 2 + e^{- 8 t}

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What is expand (e^{4t}+e^{-4t})^2 ?
The solution to expand (e^{4t}+e^{-4t})^2 is e^{8t}+2+e^{-8t}