What is expand e^x(xe^{-x}-e^x) ?

The solution to expand e^x(xe^{-x}-e^x) is x-e^{2x}

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expand e^x(xe^{-x}-e^x)

expand

e^{x} (x e^{- x} - e^{x})

x - e^{2 x}

Solution steps

e^{x} (x e^{- x} - e^{x})

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

Apply the distributive law:

a (b - c) = ab - a c

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

= e^{x} x e^{- x} - e^{x} e^{x}

= e^{x} e^{- x} x - e^{x} e^{x}

Simplify

e^{x} e^{- x} x - e^{x} e^{x} : x - e^{2 x}

= x - e^{2 x}

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What is expand e^x(xe^{-x}-e^x) ?
The solution to expand e^x(xe^{-x}-e^x) is x-e^{2x}