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

The solution to expand 1/4 (-2e^{-2x}x-e^{-2x}) is -(e^{-2x}x)/2-1/4 e^{-2x}

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expand 1/4 (-2e^{-2x}x-e^{-2x})

expand

\frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

- \frac{e ^{- 2 x} x}{2} - \frac{1}{4} e^{- 2 x}

Solution steps

\frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{4}, b = - 2 e^{- 2 x} x, c = e^{- 2 x}

= \frac{1}{4} (- 2 e^{- 2 x} x) - \frac{1}{4} e^{- 2 x}

Apply minus-plus rules

+ (- a) = - a

= - 2 \cdot \frac{1}{4} e^{- 2 x} x - \frac{1}{4} e^{- 2 x}

Simplify

- 2 \cdot \frac{1}{4} e^{- 2 x} x - \frac{1}{4} e^{- 2 x} : - \frac{e ^{- 2 x} x}{2} - \frac{1}{4} e^{- 2 x}

= - \frac{e ^{- 2 x} x}{2} - \frac{1}{4} e^{- 2 x}

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What is expand 1/4 (-2e^{-2x}x-e^{-2x}) ?
The solution to expand 1/4 (-2e^{-2x}x-e^{-2x}) is -(e^{-2x}x)/2-1/4 e^{-2x}