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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Multiply:

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

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

(5 x^{2} + 2 y) d x

3 (8 x + 5 y = 40)

δ (x + y)

\frac{x ^{6} - 1}{x - 1}

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

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