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+1/x)^9

解答

展开

(x + \frac{1}{x})^{9}

解答

x^{9} + 9 x^{7} + 36 x^{5} + 84 x^{3} + 126 x + \frac{126}{x} + \frac{84}{x ^{3}} + \frac{36}{x ^{5}} + \frac{9}{x ^{7}} + \frac{1}{x ^{9}}

求解步骤

(x + \frac{1}{x})^{9}

使用二项式定理:

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

a = x, b = \frac{1}{x}

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

展开求和

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

化简

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

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} x^{8} (\frac{1}{x})^{1} : 9 x^{7}

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} x^{7} (\frac{1}{x})^{2} : 36 x^{5}

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} x^{6} (\frac{1}{x})^{3} : 84 x^{3}

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} x^{5} (\frac{1}{x})^{4} : 126 x

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} x^{4} (\frac{1}{x})^{5} : \frac{126}{x}

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} x^{3} (\frac{1}{x})^{6} : \frac{84}{x ^{3}}

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} x^{2} (\frac{1}{x})^{7} : \frac{36}{x ^{5}}

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} x^{1} (\frac{1}{x})^{8} : \frac{9}{x ^{7}}

化简

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

= x^{9} + 9 x^{7} + 36 x^{5} + 84 x^{3} + 126 x + \frac{126}{x} + \frac{84}{x ^{3}} + \frac{36}{x ^{5}} + \frac{9}{x ^{7}} + \frac{1}{x ^{9}}

流行的例子

化简 sqrt(m)(sqrt(m)-2)

s im pl i f y m (m - 2)

展开-4/(x^2(x-2))

e x p an d - \frac{4}{x ^{2} ( x - 2 )}

展开 (x^2+4y^4+1)dx+16xy^3dy

e x p an d (x^{2} + 4 y^{4} + 1) d x + 16 x y^{3} d y

展开 ((x^7+1))/((x^2+1)(x^2+x+1))

e x p an d \frac{( x ^{7} + 1 )}{( x ^{2} + 1 ) ( x ^{2} + x + 1 )}

展开 (4x^2)/((4x+3)(x-1))

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