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}

(sin (x) - cos (x)) (2 π)

Dy (3 x - 2 y^{2} + \frac{8}{y ^{3}})

- \frac{1}{( x - 2 ) ^{2}}

\frac{( 2 x - 3 ) ( 3 x + 8 )}{( x - 6 ) ^{3}}

\frac{- \frac{12}{4} - 45}{24} - 2 (- 3 + 5 - 37 + 62 - 17)

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}