What is expand e^x(1+2xye^{-x}) ?

The solution to expand e^x(1+2xye^{-x}) is e^x+2xy

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expand e^x(1+2xye^{-x})

expand

e^{x} (1 + 2 x y e^{- x})

e^{x} + 2 x y

Solution steps

e^{x} (1 + 2 x y e^{- x})

= e^{x} (1 + 2 e^{- x} x y)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = 1, c = 2 x y e^{- x}

= e^{x} \cdot 1 + e^{x} \cdot 2 x y e^{- x}

= 1 \cdot e^{x} + 2 e^{x} e^{- x} x y

Simplify

1 \cdot e^{x} + 2 e^{x} e^{- x} x y : e^{x} + 2 x y

= e^{x} + 2 x y

\frac{3 ( 5 - 35 )}{10}

24 + 27

(x^{3} + x^{2} + x + 1)^{5}

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

\frac{( 4 x ^{2} + 3 x )}{x + 1}

What is expand e^x(1+2xye^{-x}) ?
The solution to expand e^x(1+2xye^{-x}) is e^x+2xy