What is expand 1/25 (e^{5x}*5x-e^{5x}) ?

The solution to expand 1/25 (e^{5x}*5x-e^{5x}) is (e^{5x}x)/5-1/25 e^{5x}

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expand 1/25 (e^{5x}*5x-e^{5x})

expand

\frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x})

\frac{e ^{5 x} x}{5} - \frac{1}{25} e^{5 x}

Solution steps

\frac{1}{25} (e^{5 x} \cdot 5 x - e^{5 x})

= \frac{1}{25} (5 e^{5 x} x - e^{5 x})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{25}, b = e^{5 x} \cdot 5 x, c = e^{5 x}

= \frac{1}{25} e^{5 x} \cdot 5 x - \frac{1}{25} e^{5 x}

= 5 \cdot \frac{1}{25} e^{5 x} x - \frac{1}{25} e^{5 x}

Simplify

5 \cdot \frac{1}{25} e^{5 x} x - \frac{1}{25} e^{5 x} : \frac{e ^{5 x} x}{5} - \frac{1}{25} e^{5 x}

= \frac{e ^{5 x} x}{5} - \frac{1}{25} e^{5 x}

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What is expand 1/25 (e^{5x}*5x-e^{5x}) ?
The solution to expand 1/25 (e^{5x}*5x-e^{5x}) is (e^{5x}x)/5-1/25 e^{5x}