What is expand (4((dI)/(dt))+12I)(e^{2t}) ?

The solution to expand (4((dI)/(dt))+12I)(e^{2t}) is 4e^{2t}(dI)/(dt)+12e^{2t}I

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expand (4((dI)/(dt))+12I)(e^{2t})

expand

(4 (\frac{d I}{d t}) + 12 I) (e^{2 t})

4 e^{2 t} \frac{d I}{d t} + 12 e^{2 t} I

Solution steps

(4 (\frac{d I}{d t}) + 12 I) (e^{2 t})

= (e^{2 t}) (4 (\frac{d I}{d t}) + 12 I)

Apply the distributive law:

a (b + c) = ab + a c

a = (e^{2 t}), b = 4 (\frac{d I}{d t}), c = 12 I

= (e^{2 t}) \cdot 4 (\frac{d I}{d t}) + (e^{2 t}) \cdot 12 I

= 4 (e^{2 t}) (\frac{d I}{d t}) + 12 (e^{2 t}) I

Remove parentheses:

(a) = a

= 4 e^{2 t} \frac{d I}{d t} + 12 e^{2 t} I

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What is expand (4((dI)/(dt))+12I)(e^{2t}) ?
The solution to expand (4((dI)/(dt))+12I)(e^{2t}) is 4e^{2t}(dI)/(dt)+12e^{2t}I