展开 ((8-x)^3)/(24)

解答

展开

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

- \frac{x ^{3}}{24} + x^{2} - 8 x + \frac{64}{3}

求解步骤

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

(8 - x)^{3} = 512 - 192 x + 24 x^{2} - x^{3}

= \frac{512 - 192 x + 24 x ^{2} - x ^{3}}{24}

使用分式法则:

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

\frac{512 - 192 x + 24 x ^{2} - x ^{3}}{24} = \frac{512}{24} - \frac{192 x}{24} + \frac{24 x ^{2}}{24} - \frac{x ^{3}}{24}

= \frac{512}{24} - \frac{192 x}{24} + \frac{24 x ^{2}}{24} - \frac{x ^{3}}{24}

消掉

\frac{512}{24} : \frac{64}{3}

= \frac{64}{3} - \frac{192 x}{24} + \frac{24 x ^{2}}{24} - \frac{x ^{3}}{24}

数字相除:

\frac{192}{24} = 8

= \frac{64}{3} - 8 x + \frac{24 x ^{2}}{24} - \frac{x ^{3}}{24}

数字相除:

\frac{24}{24} = 1

= \frac{64}{3} - 8 x + x^{2} - \frac{x ^{3}}{24}

改写为标准形式

= - \frac{x ^{3}}{24} + x^{2} - 8 x + \frac{64}{3}

e x p an d \frac{12 x - 52}{( x - 1 ) ( x - 6 )}

e x p an d \frac{20}{s ^{2} ( s ^{2} + s - 6 )}

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

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

e x p an d \frac{q ( a + b + c + d )}{c + d}