What is expand (2x+1)(1/3 e^{3x}) ?

The solution to expand (2x+1)(1/3 e^{3x}) is (2e^{3x}x)/3+(e^{3x})/3

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expand (2x+1)(1/3 e^{3x})

expand

(2 x + 1) (\frac{1}{3} e^{3 x})

\frac{2 e ^{3 x} x}{3} + \frac{e ^{3 x}}{3}

Solution steps

(2 x + 1) (\frac{1}{3} e^{3 x})

Apply the distributive law:

a (b + c) = ab + a c

a = (\frac{1}{3} e^{3 x}), b = 2 x, c = 1

= (\frac{1}{3} e^{3 x}) \cdot 2 x + (\frac{1}{3} e^{3 x}) \cdot 1

= 2 x (\frac{1}{3} e^{3 x}) + 1 \cdot (\frac{1}{3} e^{3 x})

Simplify

2 x (\frac{1}{3} e^{3 x}) + 1 \cdot (\frac{1}{3} e^{3 x}) : \frac{2 e ^{3 x} x}{3} + \frac{e ^{3 x}}{3}

= \frac{2 e ^{3 x} x}{3} + \frac{e ^{3 x}}{3}

4 x^{2} - 2 (1 + 3) x + 3

12 x - 8 x + 2

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

(x - 2) ln (50)

\frac{9}{( x - 7 ) ^{2}}

What is expand (2x+1)(1/3 e^{3x}) ?
The solution to expand (2x+1)(1/3 e^{3x}) is (2e^{3x}x)/3+(e^{3x})/3