展开 (x-1)(e^x+3)

解答

展开

(x - 1) (e^{x} + 3)

e^{x} x + 3 x - e^{x} - 3

求解步骤

(x - 1) (e^{x} + 3)

使用 FOIL 方法:

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

a = x, b = - 1, c = e^{x}, d = 3

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

使用加减运算法则

+ (- a) = - a

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

化简

e^{x} x + 3 x - 1 \cdot e^{x} - 1 \cdot 3 : e^{x} x + 3 x - e^{x} - 3

= e^{x} x + 3 x - e^{x} - 3

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

e x p an d \frac{A ( e ^{x} + 3 )}{e ^{x} - 1}

e x p an d (x + y = z) (x + 2 x + z + 14)

e x p an d \frac{( x - 3 ) ( x - 4 )}{( x + 1 ) ^{2}}

e x p an d \frac{4 ( s + 2 )}{( s ^{2} + 1 ) ( s - 2 )}