What is expand (a+bt)e^{3t}-2/5 e^{-2t} ?

The solution to expand (a+bt)e^{3t}-2/5 e^{-2t} is e^{3t}a+e^{3t}bt-2/5 e^{-2t}

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expand (a+bt)e^{3t}-2/5 e^{-2t}

expand

(a + b t) e^{3 t} - \frac{2}{5} e^{- 2 t}

e^{3 t} a + e^{3 t} b t - \frac{2}{5} e^{- 2 t}

Solution steps

(a + b t) e^{3 t} - \frac{2}{5} e^{- 2 t}

= e^{3 t} (a + b t) - \frac{2}{5} e^{- 2 t}

Expand

e^{3 t} (a + b t) : e^{3 t} a + e^{3 t} b t

= e^{3 t} a + e^{3 t} b t - \frac{2}{5} e^{- 2 t}

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(- sin (t) - sin (2 t)) (- sin (t) - 2 sin (2 t)) - (- cos (t) - 2 cos (2 t)) (cos (t) + cos (2 t))

What is expand (a+bt)e^{3t}-2/5 e^{-2t} ?
The solution to expand (a+bt)e^{3t}-2/5 e^{-2t} is e^{3t}a+e^{3t}bt-2/5 e^{-2t}