展开 (e^{5x}-1)(4-x^2)

解答

展开

(e^{5 x} - 1) (4 - x^{2})

4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

求解步骤

(e^{5 x} - 1) (4 - x^{2})

使用 FOIL 方法:

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

a = e^{5 x}, b = - 1, c = 4, d = - x^{2}

= e^{5 x} \cdot 4 + e^{5 x} (- x^{2}) + (- 1) \cdot 4 + (- 1) (- x^{2})

使用加减运算法则

+ (- a) = - a, (- a) (- b) = ab

= 4 e^{5 x} - e^{5 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2}

化简

4 e^{5 x} - e^{5 x} x^{2} - 1 \cdot 4 + 1 \cdot x^{2} : 4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

= 4 e^{5 x} - e^{5 x} x^{2} - 4 + x^{2}

s im pl i f y \frac{1}{2} (lo g_{6} (x) + lo g_{8} (y))

e x p an d (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2}

e x p an d \frac{2 ( 7 - 4 )}{3}

e x p an d (\frac{b}{a} (x - z) + y + c)^{3}

e x p an d l {e^{4 t} (t - cos (t))}