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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

x^{\frac{1}{3}} (x^{\frac{2}{3}} - x)

\frac{( 50 s )}{( s + 10 ) ( s + 1 )}

sin (\frac{1}{2} (x + \frac{π}{4}))

4 (a cos (2 x) + b sin (2 x))

(csc (x) + sec (x))^{2}

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