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

The solution to expand e^{2x}(e^x-e^{-x}) is e^{3x}-e^x

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

expand

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

e^{3 x} - e^{x}

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Simplify

e^{x} e^{2 x} - e^{2 x} e^{- x} : e^{3 x} - e^{x}

= e^{3 x} - e^{x}

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What is expand e^{2x}(e^x-e^{-x}) ?
The solution to expand e^{2x}(e^x-e^{-x}) is e^{3x}-e^x