What is expand (e^{3t}-e^{-3t})^2 ?

The solution to expand (e^{3t}-e^{-3t})^2 is e^{6t}-2+e^{-6t}

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expand (e^{3t}-e^{-3t})^2

expand

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

e^{6 t} - 2 + e^{- 6 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{3 t}, b = e^{- 3 t}

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

Simplify

(e^{3 t})^{2} - 2 e^{3 t} e^{- 3 t} + (e^{- 3 t})^{2} : e^{6 t} - 2 + e^{- 6 t}

= e^{6 t} - 2 + e^{- 6 t}

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What is expand (e^{3t}-e^{-3t})^2 ?
The solution to expand (e^{3t}-e^{-3t})^2 is e^{6t}-2+e^{-6t}