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 (2x-1/y)^9

解答

展开

(2 x - \frac{1}{y})^{9}

解答

512 x^{9} - \frac{2304 x ^{8}}{y} + \frac{4608 x ^{7}}{y ^{2}} - \frac{5376 x ^{6}}{y ^{3}} + \frac{4032 x ^{5}}{y ^{4}} - \frac{2016 x ^{4}}{y ^{5}} + \frac{672 x ^{3}}{y ^{6}} - \frac{144 x ^{2}}{y ^{7}} + \frac{18 x}{y ^{8}} - \frac{1}{y ^{9}}

求解步骤

(2 x - \frac{1}{y})^{9}

使用二项式定理:

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

a = 2 x, b = - \frac{1}{y}

= i = 0 \sum 9 (i 9) (2 x)^{(9 - i)} (- \frac{1}{y})^{i}

展开求和

= \frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} (- \frac{1}{y})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} (- \frac{1}{y})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} (- \frac{1}{y})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} (- \frac{1}{y})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} (- \frac{1}{y})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} (- \frac{1}{y})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} (- \frac{1}{y})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} (- \frac{1}{y})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} (- \frac{1}{y})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} (- \frac{1}{y})^{9}

化简

\frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} (- \frac{1}{y})^{0} : 512 x^{9}

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} (- \frac{1}{y})^{1} : - \frac{2304 x ^{8}}{y}

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} (- \frac{1}{y})^{2} : \frac{4608 x ^{7}}{y ^{2}}

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} (- \frac{1}{y})^{3} : - \frac{5376 x ^{6}}{y ^{3}}

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} (- \frac{1}{y})^{4} : \frac{4032 x ^{5}}{y ^{4}}

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} (- \frac{1}{y})^{5} : - \frac{2016 x ^{4}}{y ^{5}}

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} (- \frac{1}{y})^{6} : \frac{672 x ^{3}}{y ^{6}}

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} (- \frac{1}{y})^{7} : - \frac{144 x ^{2}}{y ^{7}}

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} (- \frac{1}{y})^{8} : \frac{18 x}{y ^{8}}

化简

\frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} (- \frac{1}{y})^{9} : - \frac{1}{y ^{9}}

= 512 x^{9} - \frac{2304 x ^{8}}{y} + \frac{4608 x ^{7}}{y ^{2}} - \frac{5376 x ^{6}}{y ^{3}} + \frac{4032 x ^{5}}{y ^{4}} - \frac{2016 x ^{4}}{y ^{5}} + \frac{672 x ^{3}}{y ^{6}} - \frac{144 x ^{2}}{y ^{7}} + \frac{18 x}{y ^{8}} - \frac{1}{y ^{9}}

流行的例子

展开 (50cos(8x))/((cos(x)-1)^2)

e x p an d \frac{50 cos ( 8 x )}{( cos ( x ) - 1 ) ^{2}}

展开 2((-2x+2)(2x^2-1))

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

展开 sec(x)(1-sin(2x))

e x p an d sec (x) (1 - sin (2 x))

展开 (x^2-6x+2)/((x-3)^2)

e x p an d \frac{x ^{2} - 6 x + 2}{( x - 3 ) ^{2}}

展开 ((x+2)*x^2)/((x-2)(x-1))

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