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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

(\frac{6}{D} v + \frac{6}{D} w)^{2}

(N - 4)!

(\frac{x - u}{2})^{2}

C x^{4 n} (x^{\frac{1}{4}} - 1)

\frac{2 s ^{3} + 10 s + 3}{s ^{2} ( s + 1 ) ( s + 2 )}

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