展开 (8(2-2x)^3)/3

解答

展开

\frac{8 ( 2 - 2 x ) ^{3}}{3}

- \frac{64 x ^{3}}{3} + 64 x^{2} - 64 x + \frac{64}{3}

求解步骤

\frac{8 ( 2 - 2 x ) ^{3}}{3}

(2 - 2 x)^{3} = 8 - 24 x + 24 x^{2} - 8 x^{3}

= \frac{8 ( - 8 x ^{3} + 24 x ^{2} - 24 x + 8 )}{3}

乘开

8 (8 - 24 x + 24 x^{2} - 8 x^{3}) : 64 - 192 x + 192 x^{2} - 64 x^{3}

= \frac{64 - 192 x + 192 x ^{2} - 64 x ^{3}}{3}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{64 - 192 x + 192 x ^{2} - 64 x ^{3}}{3} = \frac{64}{3} - \frac{192 x}{3} + \frac{192 x ^{2}}{3} - \frac{64 x ^{3}}{3}

= \frac{64}{3} - \frac{192 x}{3} + \frac{192 x ^{2}}{3} - \frac{64 x ^{3}}{3}

数字相除:

\frac{192}{3} = 64

= \frac{64}{3} - 64 x + 64 x^{2} - \frac{64 x ^{3}}{3}

改写为标准形式

= - \frac{64 x ^{3}}{3} + 64 x^{2} - 64 x + \frac{64}{3}

e x p an d - 4 (x + 2) - \frac{1}{3} (- 12 x = 3)

e x p an d U (- 3, 1, - 1) \cdot v (- 4, 5, 0)

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

e x p an d 3 b + (3 b - 2)

e x p an d \frac{1}{( x + 1 ) ^{6}}