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}

(2 x + 2Δ x + 3) (4 x - 5)

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(5 x^{2} - 11 y^{7})^{25}

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}