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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Simplify

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

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

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