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

The solution to expand (e^x+2)(e^x+1/3) is e^{2x}+7/3 e^x+2/3

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

expand

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

e^{2 x} + \frac{7}{3} e^{x} + \frac{2}{3}

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

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

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

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

Simplify

e^{x} e^{x} + \frac{1}{3} e^{x} + 2 e^{x} + 2 \cdot \frac{1}{3} : e^{2 x} + \frac{7}{3} e^{x} + \frac{2}{3}

= e^{2 x} + \frac{7}{3} e^{x} + \frac{2}{3}

\frac{( x + 5 ) ( x + 2 )}{x ^{2} - 7}

\frac{( 3 x ^{(2)} + 10 )}{( x ^{(2)} ( x ^{(4)} - 16 ) )}

(2 v w + w - v e^{- 2 v}) d v + v d w

e^{x} x^{2} + 2 x (e^{x} + 1)

\frac{d x}{x ( m - x )}

What is expand (e^x+2)(e^x+1/3) ?
The solution to expand (e^x+2)(e^x+1/3) is e^{2x}+7/3 e^x+2/3