What is expand (-e^{-5t}+1)e^{2t} ?

The solution to expand (-e^{-5t}+1)e^{2t} is -e^{-3t}+e^{2t}

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expand (-e^{-5t}+1)e^{2t}

expand

(- e^{- 5 t} + 1) e^{2 t}

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

Solution steps

(- e^{- 5 t} + 1) e^{2 t}

= e^{2 t} (- e^{- 5 t} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{2 t}, b = - e^{- 5 t}, c = 1

= e^{2 t} (- e^{- 5 t}) + e^{2 t} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - e^{2 t} e^{- 5 t} + 1 \cdot e^{2 t}

Simplify

- e^{2 t} e^{- 5 t} + 1 \cdot e^{2 t} : - e^{- 3 t} + e^{2 t}

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

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What is expand (-e^{-5t}+1)e^{2t} ?
The solution to expand (-e^{-5t}+1)e^{2t} is -e^{-3t}+e^{2t}