What is expand e^t(1+e^{-2t}) ?

The solution to expand e^t(1+e^{-2t}) is e^t+e^{-t}

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expand e^t(1+e^{-2t})

expand

e^{t} (1 + e^{- 2 t})

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

Solution steps

e^{t} (1 + e^{- 2 t})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{t}, b = 1, c = e^{- 2 t}

= e^{t} \cdot 1 + e^{t} e^{- 2 t}

= 1 \cdot e^{t} + e^{t} e^{- 2 t}

Simplify

1 \cdot e^{t} + e^{t} e^{- 2 t} : e^{t} + e^{- t}

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

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What is expand e^t(1+e^{-2t}) ?
The solution to expand e^t(1+e^{-2t}) is e^t+e^{-t}