What is expand (e^{-2t}+e^{-3.5t}-e^{-4t})u(t) ?

The solution to expand (e^{-2t}+e^{-3.5t}-e^{-4t})u(t) is e^{-2t}tu+e^{-3.5t}tu-e^{-4t}tu

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expand (e^{-2t}+e^{-3.5t}-e^{-4t})u(t)

expand

(e^{- 2 t} + e^{- 3.5 t} - e^{- 4 t}) u (t)

e^{- 2 t} t u + e^{- 3.5 t} t u - e^{- 4 t} t u

Solution steps

(e^{- 2 t} + e^{- 3.5 t} - e^{- 4 t}) u (t)

= (t) u (e^{- 2 t} + e^{- 3.5 t} - e^{- 4 t})

Distribute parentheses

= u (t) e^{- 2 t} + u (t) e^{- 3.5 t} + u (t) (- e^{- 4 t})

Apply minus-plus rules

+ (- a) = - a

= e^{- 2 t} (t) u + e^{- 3.5 t} (t) u - e^{- 4 t} (t) u

Remove parentheses:

(a) = a

= e^{- 2 t} t u + e^{- 3.5 t} t u - e^{- 4 t} t u

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What is expand (e^{-2t}+e^{-3.5t}-e^{-4t})u(t) ?
The solution to expand (e^{-2t}+e^{-3.5t}-e^{-4t})u(t) is e^{-2t}tu+e^{-3.5t}tu-e^{-4t}tu