What is expand e^t(-te^{-t}-e^{-t}+1) ?

The solution to expand e^t(-te^{-t}-e^{-t}+1) is -t-1+e^t

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expand e^t(-te^{-t}-e^{-t}+1)

expand

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

- t - 1 + e^{t}

Solution steps

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= - e^{t} e^{- t} t - e^{t} e^{- t} + 1 \cdot e^{t}

Simplify

- e^{t} e^{- t} t - e^{t} e^{- t} + 1 \cdot e^{t} : - t - 1 + e^{t}

= - t - 1 + e^{t}

x^{\frac{1 - 2 x}{x}} (- ln (x) + 1)

(1, \frac{13}{2}) y (6, - 4)

(2 x + 1) (2 x - 1)

(2 + \frac{1}{4} x)^{8} (2 x - \frac{3}{x})^{2}

(3 - y)^{2}

What is expand e^t(-te^{-t}-e^{-t}+1) ?
The solution to expand e^t(-te^{-t}-e^{-t}+1) is -t-1+e^t