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

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

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

expand

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

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

Solution steps

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

4 π (r^{3} + 15 r^{2} + 75 r + 125)

e^{t} (sin (t) - cos (t))

\frac{1}{s ^{2} ( s + 4 ) ^{2}}

R (0, - 2) S (- 3 - 5)

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