What is expand-1/6 (x-3*(x^2e^{-x})) ?

The solution to expand-1/6 (x-3*(x^2e^{-x})) is -x/6+(e^{-x}x^2)/2

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expand-1/6 (x-3*(x^2e^{-x}))

expand

- \frac{1}{6} (x - 3 \cdot (x^{2} e^{- x}))

- \frac{x}{6} + \frac{e ^{- x} x ^{2}}{2}

Solution steps

- \frac{1}{6} (x - 3 (x^{2} e^{- x}))

= - \frac{1}{6} (x - 3 (e^{- x} x^{2}))

Apply the distributive law:

a (b - c) = ab - a c

a = - \frac{1}{6}, b = x, c = 3 (x^{2} e^{- x})

= - \frac{1}{6} x - (- \frac{1}{6}) \cdot 3 (x^{2} e^{- x})

Apply minus-plus rules

- (- a) = a

= - \frac{1}{6} x + 3 \cdot \frac{1}{6} (e^{- x} x^{2})

Simplify

- \frac{1}{6} x + 3 \cdot \frac{1}{6} (e^{- x} x^{2}) : - \frac{x}{6} + \frac{e ^{- x} x ^{2}}{2}

= - \frac{x}{6} + \frac{e ^{- x} x ^{2}}{2}

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What is expand-1/6 (x-3*(x^2e^{-x})) ?
The solution to expand-1/6 (x-3*(x^2e^{-x})) is -x/6+(e^{-x}x^2)/2