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

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

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

expand

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

e^{- 3 t} + 3 e^{- t} + 3 e^{t} + e^{3 t}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

3 (1 + cos (θ))

(2 + 5) (3 - 2)

A (4, - 3)

\frac{6 e ^{x}}{( 6 + e ^{x} ) ^{2}}

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