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

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

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

expand

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

- t - 1

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = e^{t}, b = - t e^{- t}, c = e^{- t}

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

Apply minus-plus rules

+ (- a) = - a

= - e^{t} e^{- t} t - e^{t} e^{- t}

Simplify

- e^{t} e^{- t} t - e^{t} e^{- t} : - t - 1

= - t - 1

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