What is expand-125(-0.2e^{-0.2t}t-e^{-0.2t}) ?

The solution to expand-125(-0.2e^{-0.2t}t-e^{-0.2t}) is 25e^{-0.2t}t+125e^{-0.2t}

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expand-125(-0.2e^{-0.2t}t-e^{-0.2t})

expand

- 125 (- 0.2 e^{- 0.2 t} t - e^{- 0.2 t})

25 e^{- 0.2 t} t + 125 e^{- 0.2 t}

Solution steps

- 125 (- 0.2 e^{- 0.2 t} t - e^{- 0.2 t})

Apply the distributive law:

a (b - c) = ab - a c

a = - 125, b = - 0.2 e^{- 0.2 t} t, c = e^{- 0.2 t}

= - 125 (- 0.2 e^{- 0.2 t} t) - (- 125) e^{- 0.2 t}

Apply minus-plus rules

- (- a) = a

= 125 \cdot 0.2 e^{- 0.2 t} t + 125 e^{- 0.2 t}

Multiply the numbers:

125 \cdot 0.2 = 25

= 25 e^{- 0.2 t} t + 125 e^{- 0.2 t}

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What is expand-125(-0.2e^{-0.2t}t-e^{-0.2t}) ?
The solution to expand-125(-0.2e^{-0.2t}t-e^{-0.2t}) is 25e^{-0.2t}t+125e^{-0.2t}