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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

\frac{cos ^{3} ( n ) ( n + 1 )}{n ^{3}}

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

(2 x + cos (x)) (3 - e^{x})

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

(\frac{1}{t} - i)^{2}

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