What is expand 1/9 (e^{3t}*3t-e^{3t}) ?

The solution to expand 1/9 (e^{3t}*3t-e^{3t}) is (e^{3t}t)/3-1/9 e^{3t}

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expand 1/9 (e^{3t}*3t-e^{3t})

expand

\frac{1}{9} (e^{3 t} \cdot 3 t - e^{3 t})

\frac{e ^{3 t} t}{3} - \frac{1}{9} e^{3 t}

Solution steps

\frac{1}{9} (e^{3 t} \cdot 3 t - e^{3 t})

= \frac{1}{9} (3 e^{3 t} t - e^{3 t})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{9}, b = e^{3 t} \cdot 3 t, c = e^{3 t}

= \frac{1}{9} e^{3 t} \cdot 3 t - \frac{1}{9} e^{3 t}

= 3 \cdot \frac{1}{9} e^{3 t} t - \frac{1}{9} e^{3 t}

Simplify

3 \cdot \frac{1}{9} e^{3 t} t - \frac{1}{9} e^{3 t} : \frac{e ^{3 t} t}{3} - \frac{1}{9} e^{3 t}

= \frac{e ^{3 t} t}{3} - \frac{1}{9} e^{3 t}

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What is expand 1/9 (e^{3t}*3t-e^{3t}) ?
The solution to expand 1/9 (e^{3t}*3t-e^{3t}) is (e^{3t}t)/3-1/9 e^{3t}