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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

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