zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

展开 (x/2-y/3)^6

解答

展开

(\frac{x}{2} - \frac{y}{3})^{6}

解答

\frac{729 x ^{6} + 64 y ^{6}}{46656} - \frac{x ^{5} y}{16} + \frac{5 x ^{4} y ^{2}}{48} - \frac{5 x ^{3} y ^{3}}{54} + \frac{5 x ^{2} y ^{4}}{108} - \frac{x y ^{5}}{81}

求解步骤

(\frac{x}{2} - \frac{y}{3})^{6}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{x}{2}, b = - \frac{y}{3}

= i = 0 \sum 6 (i 6) (\frac{x}{2})^{(6 - i)} (- \frac{y}{3})^{i}

展开求和

= \frac{6 !}{0 ! ( 6 - 0 ) !} (\frac{x}{2})^{6} (- \frac{y}{3})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (\frac{x}{2})^{5} (- \frac{y}{3})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (\frac{x}{2})^{4} (- \frac{y}{3})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (\frac{x}{2})^{3} (- \frac{y}{3})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (\frac{x}{2})^{2} (- \frac{y}{3})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (\frac{x}{2})^{1} (- \frac{y}{3})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (\frac{x}{2})^{0} (- \frac{y}{3})^{6}

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} (\frac{x}{2})^{6} (- \frac{y}{3})^{0} : \frac{x ^{6}}{64}

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} (\frac{x}{2})^{5} (- \frac{y}{3})^{1} : - \frac{x ^{5} y}{16}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} (\frac{x}{2})^{4} (- \frac{y}{3})^{2} : \frac{5 x ^{4} y ^{2}}{48}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} (\frac{x}{2})^{3} (- \frac{y}{3})^{3} : - \frac{5 x ^{3} y ^{3}}{54}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} (\frac{x}{2})^{2} (- \frac{y}{3})^{4} : \frac{5 x ^{2} y ^{4}}{108}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} (\frac{x}{2})^{1} (- \frac{y}{3})^{5} : - \frac{x y ^{5}}{81}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} (\frac{x}{2})^{0} (- \frac{y}{3})^{6} : \frac{y ^{6}}{729}

= \frac{x ^{6}}{64} - \frac{x ^{5} y}{16} + \frac{5 x ^{4} y ^{2}}{48} - \frac{5 x ^{3} y ^{3}}{54} + \frac{5 x ^{2} y ^{4}}{108} - \frac{x y ^{5}}{81} + \frac{y ^{6}}{729}

化简

\frac{x ^{6}}{64} - \frac{x ^{5} y}{16} + \frac{5 x ^{4} y ^{2}}{48} - \frac{5 x ^{3} y ^{3}}{54} + \frac{5 x ^{2} y ^{4}}{108} - \frac{x y ^{5}}{81} + \frac{y ^{6}}{729} : \frac{729 x ^{6} + 64 y ^{6}}{46656} - \frac{x ^{5} y}{16} + \frac{5 x ^{4} y ^{2}}{48} - \frac{5 x ^{3} y ^{3}}{54} + \frac{5 x ^{2} y ^{4}}{108} - \frac{x y ^{5}}{81}

= \frac{729 x ^{6} + 64 y ^{6}}{46656} - \frac{x ^{5} y}{16} + \frac{5 x ^{4} y ^{2}}{48} - \frac{5 x ^{3} y ^{3}}{54} + \frac{5 x ^{2} y ^{4}}{108} - \frac{x y ^{5}}{81}

流行的例子

展开 (-3/4 x+7/8 y=-11/5)*1/3

e x p an d (- \frac{3}{4} x + \frac{7}{8} y = - \frac{11}{5}) \cdot \frac{1}{3}

化简 (x-13i)(x+5+10i)(x-5-10i)

s im pl i f y (x - 13 i) (x + 5 + 10 i) (x - 5 - 10 i)

展开 (45(e^2-1))/2

e x p an d \frac{45 ( e ^{2} - 1 )}{2}

展开 (((x-1)^2))/x

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

展开 (3(n+1)(2n+1))/(2n)

e x p an d \frac{3 ( n + 1 ) ( 2 n + 1 )}{2 n}