What is expand (e^{-x}+e^x)^3 ?

The solution to expand (e^{-x}+e^x)^3 is e^{-3x}+3e^{-x}+3e^x+e^{3x}

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expand (e^{-x}+e^x)^3

expand

(e^{- x} + e^{x})^{3}

e^{- 3 x} + 3 e^{- x} + 3 e^{x} + e^{3 x}

Solution steps

(e^{- x} + e^{x})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

= (e^{- x})^{3} + 3 (e^{- x})^{2} e^{x} + 3 e^{- x} (e^{x})^{2} + (e^{x})^{3}

Simplify

(e^{- x})^{3} + 3 (e^{- x})^{2} e^{x} + 3 e^{- x} (e^{x})^{2} + (e^{x})^{3} : e^{- 3 x} + 3 e^{- x} + 3 e^{x} + e^{3 x}

= e^{- 3 x} + 3 e^{- x} + 3 e^{x} + e^{3 x}

11 (7 + 2)

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What is expand (e^{-x}+e^x)^3 ?
The solution to expand (e^{-x}+e^x)^3 is e^{-3x}+3e^{-x}+3e^x+e^{3x}