What is expand (1-e^{-10t})U(t) ?

The solution to expand (1-e^{-10t})U(t) is tU-e^{-10t}tU

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expand (1-e^{-10t})U(t)

expand

(1 - e^{- 10 t}) U (t)

t U - e^{- 10 t} t U

Solution steps

(1 - e^{- 10 t}) U (t)

= (t) U (1 - e^{- 10 t})

Apply the distributive law:

a (b - c) = ab - a c

a = U (t), b = 1, c = e^{- 10 t}

= U (t) \cdot 1 - U (t) e^{- 10 t}

= 1 \cdot (t) U - e^{- 10 t} (t) U

Simplify

1 \cdot (t) U - e^{- 10 t} (t) U : t U - e^{- 10 t} t U

= t U - e^{- 10 t} t U

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What is expand (1-e^{-10t})U(t) ?
The solution to expand (1-e^{-10t})U(t) is tU-e^{-10t}tU