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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Remove parentheses:

(a) = a

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

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l imh \Rightarrow 0 (8 + h) 2 - 64 h

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