What is expand 1/3 e^{3x}(x-1/3) ?

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

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expand 1/3 e^{3x}(x-1/3)

expand

\frac{1}{3} e^{3 x} (x - \frac{1}{3})

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

Solution steps

\frac{1}{3} e^{3 x} (x - \frac{1}{3})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{3} e^{3 x}, b = x, c = \frac{1}{3}

= \frac{1}{3} e^{3 x} x - \frac{1}{3} e^{3 x} \frac{1}{3}

= \frac{1}{3} e^{3 x} x - \frac{1}{3} \cdot \frac{1}{3} e^{3 x}

Simplify

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

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

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