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

The solution to expand 1/9 (e^{3x}*3x-e^{3x})(e^x) is (e^{4x}x)/3-1/9 e^{4x}

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

expand

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

\frac{e ^{4 x} x}{3} - \frac{1}{9} e^{4 x}

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{9} (e^{x}), b = e^{3 x} \cdot 3 x, c = e^{3 x}

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

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

Simplify

3 \cdot \frac{1}{9} e^{3 x} x (e^{x}) - \frac{1}{9} e^{3 x} (e^{x}) : \frac{e ^{4 x} x}{3} - \frac{1}{9} e^{4 x}

= \frac{e ^{4 x} x}{3} - \frac{1}{9} e^{4 x}

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What is expand 1/9 (e^{3x}*3x-e^{3x})(e^x) ?
The solution to expand 1/9 (e^{3x}*3x-e^{3x})(e^x) is (e^{4x}x)/3-1/9 e^{4x}