What is expand e^y(-e^{-y}y-e^{-y}) ?

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

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expand e^y(-e^{-y}y-e^{-y})

expand

e^{y} (- e^{- y} y - e^{- y})

- y - 1

Solution steps

e^{y} (- e^{- y} y - e^{- y})

Apply the distributive law:

a (b - c) = ab - a c

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

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

Apply minus-plus rules

+ (- a) = - a

= - e^{y} e^{- y} y - e^{y} e^{- y}

Simplify

- e^{y} e^{- y} y - e^{y} e^{- y} : - y - 1

= - y - 1

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