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

The solution to expand-e^x(e^{2x}-e^{-x}) is -e^{3x}+1

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

expand

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

- e^{3 x} + 1

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

Apply minus-plus rules

- (- a) = a

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

Simplify

- e^{x} e^{2 x} + e^{x} e^{- x} : - e^{3 x} + 1

= - e^{3 x} + 1

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What is expand-e^x(e^{2x}-e^{-x}) ?
The solution to expand-e^x(e^{2x}-e^{-x}) is -e^{3x}+1