What is expand-e^x(1+e^x) ?

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

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expand-e^x(1+e^x)

expand

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

- e^{x} - e^{2 x}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

= - e^{x} \cdot 1 + (- e^{x}) e^{x}

Apply minus-plus rules

+ (- a) = - a

= - 1 \cdot e^{x} - e^{x} e^{x}

Simplify

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

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

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