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

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

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

expand

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

e^{4 x} + 2 e^{x} + e^{- 2 x}

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{2 x}, b = e^{- x}

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

Simplify

(e^{2 x})^{2} + 2 e^{2 x} e^{- x} + (e^{- x})^{2} : e^{4 x} + 2 e^{x} + e^{- 2 x}

= e^{4 x} + 2 e^{x} + e^{- 2 x}

(x^{2} + x) d x

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