展开 (e^x+2)(e^x+1/3)

解答

展开

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

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

求解步骤

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

使用 FOIL 方法:

(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}

化简

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}

e x p an d \frac{( x + 5 ) ( x + 2 )}{x ^{2} - 7}

e x p an d \frac{( 3 x ^{(2)} + 10 )}{( x ^{(2)} ( x ^{(4)} - 16 ) )}

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

e x p an d e^{x} x^{2} + 2 x (e^{x} + 1)

e x p an d \frac{d x}{x ( m - x )}