What is expand 4000(-x/4+3)e^{-x/4-1} ?

The solution to expand 4000(-x/4+3)e^{-x/4-1} is -1000e^{-x/4-1}x+12000e^{-x/4-1}

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expand 4000(-x/4+3)e^{-x/4-1}

expand

4000 (- \frac{x}{4} + 3) e^{- \frac{x}{4} - 1}

- 1000 e^{- \frac{x}{4} - 1} x + 12000 e^{- \frac{x}{4} - 1}

Solution steps

4000 (- \frac{x}{4} + 3) e^{- \frac{x}{4} - 1}

= 4000 e^{- \frac{x}{4} - 1} (- \frac{x}{4} + 3)

Apply the distributive law:

a (b + c) = ab + a c

a = 4000 e^{- \frac{x}{4} - 1}, b = - \frac{x}{4}, c = 3

= 4000 e^{- \frac{x}{4} - 1} (- \frac{x}{4}) + 4000 e^{- \frac{x}{4} - 1} \cdot 3

Apply minus-plus rules

+ (- a) = - a

= - 4000 e^{- \frac{x}{4} - 1} \frac{x}{4} + 4000 \cdot 3 e^{- \frac{x}{4} - 1}

Simplify

- 4000 e^{- \frac{x}{4} - 1} \frac{x}{4} + 4000 \cdot 3 e^{- \frac{x}{4} - 1} : - 1000 e^{- \frac{x}{4} - 1} x + 12000 e^{- \frac{x}{4} - 1}

= - 1000 e^{- \frac{x}{4} - 1} x + 12000 e^{- \frac{x}{4} - 1}

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What is expand 4000(-x/4+3)e^{-x/4-1} ?
The solution to expand 4000(-x/4+3)e^{-x/4-1} is -1000e^{-x/4-1}x+12000e^{-x/4-1}