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受欢迎的代数 >

展开 (x^2-1/x)^9

解答

展开

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

解答

x^{18} - 9 x^{15} + 36 x^{12} - 84 x^{9} + 126 x^{6} - 126 x^{3} + 84 - \frac{36}{x ^{3}} + \frac{9}{x ^{6}} - \frac{1}{x ^{9}}

求解步骤

(x^{2} - \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^{2}, b = - \frac{1}{x}

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

展开求和

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

化简

\frac{9 !}{0 ! ( 9 - 0 ) !} (x^{2})^{9} (- \frac{1}{x})^{0} : x^{18}

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} (x^{2})^{8} (- \frac{1}{x})^{1} : - 9 x^{15}

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} (x^{2})^{7} (- \frac{1}{x})^{2} : 36 x^{12}

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} (x^{2})^{6} (- \frac{1}{x})^{3} : - 84 x^{9}

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} (x^{2})^{5} (- \frac{1}{x})^{4} : 126 x^{6}

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} (x^{2})^{4} (- \frac{1}{x})^{5} : - 126 x^{3}

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} (x^{2})^{3} (- \frac{1}{x})^{6} : 84

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} (x^{2})^{2} (- \frac{1}{x})^{7} : - \frac{36}{x ^{3}}

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} (x^{2})^{1} (- \frac{1}{x})^{8} : \frac{9}{x ^{6}}

化简

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

= x^{18} - 9 x^{15} + 36 x^{12} - 84 x^{9} + 126 x^{6} - 126 x^{3} + 84 - \frac{36}{x ^{3}} + \frac{9}{x ^{6}} - \frac{1}{x ^{9}}

流行的例子

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化简 (6-2i)^4

s im pl i f y (6 - 2 i)^{4}

展开 (x+3)/(y(z+5))

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展开 (2a+3b)left(5a-b)

e x p an d (2 a + 3 b) l e f t (5 a - b)

展开 (x^2-1/x)^2

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