What is expand e^{6t}(6e^{-6t}+C) ?

The solution to expand e^{6t}(6e^{-6t}+C) is 6+e^{6t}C

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expand e^{6t}(6e^{-6t}+C)

expand

e^{6 t} (6 e^{- 6 t} + C)

6 + e^{6 t} C

Solution steps

e^{6 t} (6 e^{- 6 t} + C)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{6 t}, b = 6 e^{- 6 t}, c = C

= e^{6 t} \cdot 6 e^{- 6 t} + e^{6 t} C

= 6 e^{6 t} e^{- 6 t} + e^{6 t} C

6 e^{6 t} e^{- 6 t} = 6

= 6 + e^{6 t} C

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What is expand e^{6t}(6e^{-6t}+C) ?
The solution to expand e^{6t}(6e^{-6t}+C) is 6+e^{6t}C