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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = e^{3 t}, b = t, c = e^{- 2 t}

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

e^{3 t} e^{- 2 t} = e^{t}

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

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