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

Remove parentheses:

(a) = a

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

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

\frac{1}{( x ^{4} + 1 ) ^{2}}

(x - 2) (\cdot + 2)

\frac{8 a ^{2} b - 32 b ^{3}}{x ^{2} + 2 ( a - 2 b ) x - 8 ab}

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