What is expand 2(11/5 e^{-2t}+4/5 e^{3t}) ?

The solution to expand 2(11/5 e^{-2t}+4/5 e^{3t}) is 22/5 e^{-2t}+8/5 e^{3t}

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expand 2(11/5 e^{-2t}+4/5 e^{3t})

expand

2 (\frac{11}{5} e^{- 2 t} + \frac{4}{5} e^{3 t})

\frac{22}{5} e^{- 2 t} + \frac{8}{5} e^{3 t}

Solution steps

2 (\frac{11}{5} e^{- 2 t} + \frac{4}{5} e^{3 t})

Apply the distributive law:

a (b + c) = ab + a c

a = 2, b = \frac{11}{5} e^{- 2 t}, c = \frac{4}{5} e^{3 t}

= 2 \cdot \frac{11}{5} e^{- 2 t} + 2 \cdot \frac{4}{5} e^{3 t}

Simplify

2 \cdot \frac{11}{5} e^{- 2 t} + 2 \cdot \frac{4}{5} e^{3 t} : \frac{22}{5} e^{- 2 t} + \frac{8}{5} e^{3 t}

= \frac{22}{5} e^{- 2 t} + \frac{8}{5} e^{3 t}

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What is expand 2(11/5 e^{-2t}+4/5 e^{3t}) ?
The solution to expand 2(11/5 e^{-2t}+4/5 e^{3t}) is 22/5 e^{-2t}+8/5 e^{3t}