What is expand (-1/8 e^{-4x}+1/12 e^{-3x})(2/3 e^{2x}) ?

The solution to expand (-1/8 e^{-4x}+1/12 e^{-3x})(2/3 e^{2x}) is -(e^{-2x})/(12)+(e^{-x})/(18)

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expand (-1/8 e^{-4x}+1/12 e^{-3x})(2/3 e^{2x})

expand

(- \frac{1}{8} e^{- 4 x} + \frac{1}{12} e^{- 3 x}) (\frac{2}{3} e^{2 x})

- \frac{e ^{- 2 x}}{12} + \frac{e ^{- x}}{18}

Solution steps

(- \frac{1}{8} e^{- 4 x} + \frac{1}{12} e^{- 3 x}) (\frac{2}{3} e^{2 x})

Apply the distributive law:

a (b + c) = ab + a c

a = (\frac{2}{3} e^{2 x}), b = - \frac{1}{8} e^{- 4 x}, c = \frac{1}{12} e^{- 3 x}

= (\frac{2}{3} e^{2 x}) (- \frac{1}{8} e^{- 4 x}) + (\frac{2}{3} e^{2 x}) \frac{1}{12} e^{- 3 x}

Apply minus-plus rules

+ (- a) = - a

= - \frac{1}{8} e^{- 4 x} (\frac{2}{3} e^{2 x}) + \frac{1}{12} e^{- 3 x} (\frac{2}{3} e^{2 x})

Simplify

- \frac{1}{8} e^{- 4 x} (\frac{2}{3} e^{2 x}) + \frac{1}{12} e^{- 3 x} (\frac{2}{3} e^{2 x}) : - \frac{e ^{- 2 x}}{12} + \frac{e ^{- x}}{18}

= - \frac{e ^{- 2 x}}{12} + \frac{e ^{- x}}{18}

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What is expand (-1/8 e^{-4x}+1/12 e^{-3x})(2/3 e^{2x}) ?
The solution to expand (-1/8 e^{-4x}+1/12 e^{-3x})(2/3 e^{2x}) is -(e^{-2x})/(12)+(e^{-x})/(18)