展开 (2x-3)(2-1/2 x)^5

解答

展开

(2 x - 3) (2 - \frac{1}{2} x)^{5}

184 x - 140 x^{2} + 55 x^{3} - \frac{95 x ^{4}}{8} + \frac{43 x ^{5}}{32} - \frac{x ^{6}}{16} - 96

求解步骤

(2 x - 3) (2 - \frac{1}{2} x)^{5}

= (2 - \frac{1}{2} x)^{5} (2 x - 3)

使用分配律:

a (b - c) = ab - a c

(2 - \frac{1}{2} x)^{5} (2 x - 3) = (2 - \frac{1}{2} x)^{5} \cdot 2 x - (2 - \frac{1}{2} x)^{5} \cdot 3

= (2 - \frac{1}{2} x)^{5} \cdot 2 x - (2 - \frac{1}{2} x)^{5} \cdot 3

= 2 x (2 - \frac{1}{2} x)^{5} - 3 (2 - \frac{1}{2} x)^{5}

展开

2 x (2 - \frac{1}{2} x)^{5} : 64 x - 80 x^{2} + 40 x^{3} - 10 x^{4} + \frac{5 x ^{5}}{4} - \frac{x ^{6}}{16}

= 64 x - 80 x^{2} + 40 x^{3} - 10 x^{4} + \frac{5 x ^{5}}{4} - \frac{x ^{6}}{16} - 3 (2 - \frac{1}{2} x)^{5}

展开

- 3 (2 - \frac{1}{2} x)^{5} : - 96 + 120 x - 60 x^{2} + 15 x^{3} - \frac{15 x ^{4}}{8} + \frac{3 x ^{5}}{32}

= 64 x - 80 x^{2} + 40 x^{3} - 10 x^{4} + \frac{5 x ^{5}}{4} - \frac{x ^{6}}{16} - 96 + 120 x - 60 x^{2} + 15 x^{3} - \frac{15 x ^{4}}{8} + \frac{3 x ^{5}}{32}

化简

64 x - 80 x^{2} + 40 x^{3} - 10 x^{4} + \frac{5 x ^{5}}{4} - \frac{x ^{6}}{16} - 96 + 120 x - 60 x^{2} + 15 x^{3} - \frac{15 x ^{4}}{8} + \frac{3 x ^{5}}{32} : 184 x - 140 x^{2} + 55 x^{3} - \frac{95 x ^{4}}{8} + \frac{43 x ^{5}}{32} - \frac{x ^{6}}{16} - 96

= 184 x - 140 x^{2} + 55 x^{3} - \frac{95 x ^{4}}{8} + \frac{43 x ^{5}}{32} - \frac{x ^{6}}{16} - 96

s im pl i f y 5 (\frac{x ^{2}}{2} - \frac{2 x ^{3}}{3}) + 3000

e x p an d \frac{5 ( x + h ) + 1 - 5 x + 1}{h}

e x p an d (2 - 2 π x)^{2}

e x p an d - \frac{5}{12 ( x + 2 )} + \frac{5 x - 8}{12 ( x ^{2} - 2 x + 4 )}

e x p an d (x^{2} + 1) 3 x^{2} + 2