What is expand (x^2+y^2)e^{-x^2-4y^2} ?

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

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expand (x^2+y^2)e^{-x^2-4y^2}

expand

(x^{2} + y^{2}) e^{- x^{2} - 4 y^{2}}

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

Solution steps

(x^{2} + y^{2}) e^{- x^{2} - 4 y^{2}}

= e^{- x^{2} - 4 y^{2}} (x^{2} + y^{2})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{- x^{2} - 4 y^{2}}, b = x^{2}, c = y^{2}

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

(2 + x) e^{x}

(x + 5 + 2 i) (x + 5 - 2 i) (x + 1 - 3 i) (x + 1 + 3 i)

- \frac{4}{( 2 s + 1 ) ( s + 2 )}

(x^{3} - (\frac{3}{x}) + 5) (x^{2} + 4 x + 7)

\frac{( 3 - x ) d x}{x ^{3} + 4 x ^{2} + 3 x}

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