What is expand 2y(1-2x^2)e^{-x^2-y^2} ?

The solution to expand 2y(1-2x^2)e^{-x^2-y^2} is 2e^{-x^2-y^2}y-4e^{-x^2-y^2}yx^2

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expand 2y(1-2x^2)e^{-x^2-y^2}

expand

2 y (1 - 2 x^{2}) e^{- x^{2} - y^{2}}

2 e^{- x^{2} - y^{2}} y - 4 e^{- x^{2} - y^{2}} y x^{2}

Solution steps

2 y (1 - 2 x^{2}) e^{- x^{2} - y^{2}}

= 2 e^{- x^{2} - y^{2}} y (1 - 2 x^{2})

Apply the distributive law:

a (b - c) = ab - a c

a = 2 y e^{- x^{2} - y^{2}}, b = 1, c = 2 x^{2}

= 2 y e^{- x^{2} - y^{2}} \cdot 1 - 2 y e^{- x^{2} - y^{2}} \cdot 2 x^{2}

= 2 \cdot 1 \cdot e^{- x^{2} - y^{2}} y - 2 \cdot 2 e^{- x^{2} - y^{2}} y x^{2}

Simplify

2 \cdot 1 \cdot e^{- x^{2} - y^{2}} y - 2 \cdot 2 e^{- x^{2} - y^{2}} y x^{2} : 2 e^{- x^{2} - y^{2}} y - 4 e^{- x^{2} - y^{2}} y x^{2}

= 2 e^{- x^{2} - y^{2}} y - 4 e^{- x^{2} - y^{2}} y x^{2}

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What is expand 2y(1-2x^2)e^{-x^2-y^2} ?
The solution to expand 2y(1-2x^2)e^{-x^2-y^2} is 2e^{-x^2-y^2}y-4e^{-x^2-y^2}yx^2