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

The solution to expand (1-e^{-2t})u*(t) is tu-e^{-2t}tu

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expand (1-e^{-2t})u*(t)

expand

(1 - e^{- 2 t}) u \cdot (t)

t u - e^{- 2 t} t u

Solution steps

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

= (t) u (1 - e^{- 2 t})

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Simplify

1 \cdot (t) u - e^{- 2 t} (t) u : t u - e^{- 2 t} t u

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

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