展开 ((12-x)^3)/3

解答

展开

\frac{( 12 - x ) ^{3}}{3}

- \frac{x ^{3}}{3} + 12 x^{2} - 144 x + 576

求解步骤

\frac{( 12 - x ) ^{3}}{3}

(12 - x)^{3} = 1728 - 432 x + 36 x^{2} - x^{3}

= \frac{1728 - 432 x + 36 x ^{2} - x ^{3}}{3}

使用分式法则:

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

\frac{1728 - 432 x + 36 x ^{2} - x ^{3}}{3} = \frac{1728}{3} - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

= \frac{1728}{3} - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

数字相除:

\frac{1728}{3} = 576

= 576 - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

数字相除:

\frac{432}{3} = 144

= 576 - 144 x + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

数字相除:

\frac{36}{3} = 12

= 576 - 144 x + 12 x^{2} - \frac{x ^{3}}{3}

改写为标准形式

= - \frac{x ^{3}}{3} + 12 x^{2} - 144 x + 576

e x p an d \frac{1}{( 4 s ^{2} + 4 s + 5 ) ^{2}}

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

e x p an d \frac{( 10 x - 1 ) ^{2}}{100}

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

e x p an d (1, 2, 3) x (- 2, - 2, 4)