What is expand x*e^{x+2y}(1+2y) ?

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

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expand x*e^{x+2y}(1+2y)

expand

x \cdot e^{x + 2 y} (1 + 2 y)

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Multiply:

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

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

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