What is expand e^x(y+y^2xe^{-x}) ?

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

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expand e^x(y+y^2xe^{-x})

expand

e^{x} (y + y^{2} x e^{- x})

e^{x} y + x y^{2}

Solution steps

e^{x} (y + y^{2} x e^{- x})

= e^{x} (y + e^{- x} x y^{2})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = y, c = y^{2} x e^{- x}

= e^{x} y + e^{x} y^{2} x e^{- x}

= e^{x} y + e^{x} e^{- x} x y^{2}

e^{x} e^{- x} x y^{2} = x y^{2}

= e^{x} y + x y^{2}

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