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

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

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

expand

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

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

Solution steps

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

\frac{x ^{2} + 6 x + 13}{2 ( x + 3 )}

\frac{( x + 1 )}{x ^{2} ( x + 3 )}

\frac{2 x + 3}{( x - 4 ) ( x - 3 )}

\frac{x ^{2}}{( x - 1 ) ^{4}}

x^{\circ - 1} (x + 2)

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