What is expand 1/4 (e^{2t}*2t-e^{2t}) ?

The solution to expand 1/4 (e^{2t}*2t-e^{2t}) is (e^{2t}t)/2-1/4 e^{2t}

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expand 1/4 (e^{2t}*2t-e^{2t})

expand

\frac{1}{4} (e^{2 t} \cdot 2 t - e^{2 t})

\frac{e ^{2 t} t}{2} - \frac{1}{4} e^{2 t}

Solution steps

\frac{1}{4} (e^{2 t} \cdot 2 t - e^{2 t})

= \frac{1}{4} (2 e^{2 t} t - e^{2 t})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{4}, b = e^{2 t} \cdot 2 t, c = e^{2 t}

= \frac{1}{4} e^{2 t} \cdot 2 t - \frac{1}{4} e^{2 t}

= 2 \cdot \frac{1}{4} e^{2 t} t - \frac{1}{4} e^{2 t}

Simplify

2 \cdot \frac{1}{4} e^{2 t} t - \frac{1}{4} e^{2 t} : \frac{e ^{2 t} t}{2} - \frac{1}{4} e^{2 t}

= \frac{e ^{2 t} t}{2} - \frac{1}{4} e^{2 t}

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What is expand 1/4 (e^{2t}*2t-e^{2t}) ?
The solution to expand 1/4 (e^{2t}*2t-e^{2t}) is (e^{2t}t)/2-1/4 e^{2t}