What is expand (xy-x^3-y^3)e^{-x^2-y^2} ?

The solution to expand (xy-x^3-y^3)e^{-x^2-y^2} is e^{-x^2-y^2}xy-e^{-x^2-y^2}x^3-e^{-x^2-y^2}y^3

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expand (xy-x^3-y^3)e^{-x^2-y^2}

expand

(x y - x^{3} - y^{3}) e^{- x^{2} - y^{2}}

e^{- x^{2} - y^{2}} x y - e^{- x^{2} - y^{2}} x^{3} - e^{- x^{2} - y^{2}} y^{3}

Solution steps

(x y - x^{3} - y^{3}) e^{- x^{2} - y^{2}}

= e^{- x^{2} - y^{2}} (x y - x^{3} - y^{3})

Distribute parentheses

= e^{- x^{2} - y^{2}} x y + e^{- x^{2} - y^{2}} (- x^{3}) + e^{- x^{2} - y^{2}} (- y^{3})

Apply minus-plus rules

+ (- a) = - a

= e^{- x^{2} - y^{2}} x y - e^{- x^{2} - y^{2}} x^{3} - e^{- x^{2} - y^{2}} y^{3}

\frac{2015 x - x ^{2} - 2014}{2015 ( x ^{2} + 2014 )}

\frac{2 s}{( x + 4 ) ( x + 5 )}

A (- 3, 5) B (7, - 3)

(x - 2) tan^{2} (3 x - 21)

cos (x) sin (x) (tan (x) + csc (x))

What is expand (xy-x^3-y^3)e^{-x^2-y^2} ?
The solution to expand (xy-x^3-y^3)e^{-x^2-y^2} is e^{-x^2-y^2}xy-e^{-x^2-y^2}x^3-e^{-x^2-y^2}y^3