What is expand (e^{20x}+e^{-20x})^2 ?

The solution to expand (e^{20x}+e^{-20x})^2 is e^{40x}+2+e^{-40x}

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expand (e^{20x}+e^{-20x})^2

expand

(e^{20 x} + e^{- 20 x})^{2}

e^{40 x} + 2 + e^{- 40 x}

Solution steps

(e^{20 x} + e^{- 20 x})^{2}

Apply Perfect Square Formula:

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

a = e^{20 x}, b = e^{- 20 x}

= (e^{20 x})^{2} + 2 e^{20 x} e^{- 20 x} + (e^{- 20 x})^{2}

Simplify

(e^{20 x})^{2} + 2 e^{20 x} e^{- 20 x} + (e^{- 20 x})^{2} : e^{40 x} + 2 + e^{- 40 x}

= e^{40 x} + 2 + e^{- 40 x}

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What is expand (e^{20x}+e^{-20x})^2 ?
The solution to expand (e^{20x}+e^{-20x})^2 is e^{40x}+2+e^{-40x}