What is expand (5(3-e^{2t})e^{-5t})/2 ?

The solution to expand (5(3-e^{2t})e^{-5t})/2 is (15e^{-5t})/2-(5e^{-3t})/2

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expand (5(3-e^{2t})e^{-5t})/2

expand

\frac{5 ( 3 - e ^{2 t} ) e ^{- 5 t}}{2}

\frac{15 e ^{- 5 t}}{2} - \frac{5 e ^{- 3 t}}{2}

Solution steps

\frac{5 ( 3 - e ^{2 t} ) e ^{- 5 t}}{2}

Expand

5 (3 - e^{2 t}) e^{- 5 t} : 15 e^{- 5 t} - 5 e^{- 3 t}

= \frac{15 e ^{- 5 t} - 5 e ^{- 3 t}}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{15 e ^{- 5 t} - 5 e ^{- 3 t}}{2} = \frac{15 e ^{- 5 t}}{2} - \frac{5 e ^{- 3 t}}{2}

= \frac{15 e ^{- 5 t}}{2} - \frac{5 e ^{- 3 t}}{2}

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What is expand (5(3-e^{2t})e^{-5t})/2 ?
The solution to expand (5(3-e^{2t})e^{-5t})/2 is (15e^{-5t})/2-(5e^{-3t})/2