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受欢迎的代数 >

展开 (1/(2x)-4)^{11}

解答

展开

(\frac{1}{2 x} - 4)^{11}

解答

\frac{1}{2048 x ^{11}} - \frac{11}{256 x ^{10}} + \frac{55}{32 x ^{9}} - \frac{165}{4 x ^{8}} + \frac{660}{x ^{7}} - \frac{7392}{x ^{6}} + \frac{59136}{x ^{5}} - \frac{337920}{x ^{4}} + \frac{1351680}{x ^{3}} - \frac{3604480}{x ^{2}} + \frac{5767168}{x} - 4194304

求解步骤

(\frac{1}{2 x} - 4)^{11}

使用二项式定理:

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

a = \frac{1}{2 x}, b = - 4

= i = 0 \sum 11 (i 11) (\frac{1}{2 x})^{(11 - i)} (- 4)^{i}

展开求和

= \frac{11 !}{0 ! ( 11 - 0 ) !} (\frac{1}{2 x})^{11} (- 4)^{0} + \frac{11 !}{1 ! ( 11 - 1 ) !} (\frac{1}{2 x})^{10} (- 4)^{1} + \frac{11 !}{2 ! ( 11 - 2 ) !} (\frac{1}{2 x})^{9} (- 4)^{2} + \frac{11 !}{3 ! ( 11 - 3 ) !} (\frac{1}{2 x})^{8} (- 4)^{3} + \frac{11 !}{4 ! ( 11 - 4 ) !} (\frac{1}{2 x})^{7} (- 4)^{4} + \frac{11 !}{5 ! ( 11 - 5 ) !} (\frac{1}{2 x})^{6} (- 4)^{5} + \frac{11 !}{6 ! ( 11 - 6 ) !} (\frac{1}{2 x})^{5} (- 4)^{6} + \frac{11 !}{7 ! ( 11 - 7 ) !} (\frac{1}{2 x})^{4} (- 4)^{7} + \frac{11 !}{8 ! ( 11 - 8 ) !} (\frac{1}{2 x})^{3} (- 4)^{8} + \frac{11 !}{9 ! ( 11 - 9 ) !} (\frac{1}{2 x})^{2} (- 4)^{9} + \frac{11 !}{10 ! ( 11 - 10 ) !} (\frac{1}{2 x})^{1} (- 4)^{10} + \frac{11 !}{11 ! ( 11 - 11 ) !} (\frac{1}{2 x})^{0} (- 4)^{11}

化简

\frac{11 !}{0 ! ( 11 - 0 ) !} (\frac{1}{2 x})^{11} (- 4)^{0} : \frac{1}{2048 x ^{11}}

化简

\frac{11 !}{1 ! ( 11 - 1 ) !} (\frac{1}{2 x})^{10} (- 4)^{1} : - \frac{11}{256 x ^{10}}

化简

\frac{11 !}{2 ! ( 11 - 2 ) !} (\frac{1}{2 x})^{9} (- 4)^{2} : \frac{55}{32 x ^{9}}

化简

\frac{11 !}{3 ! ( 11 - 3 ) !} (\frac{1}{2 x})^{8} (- 4)^{3} : - \frac{165}{4 x ^{8}}

化简

\frac{11 !}{4 ! ( 11 - 4 ) !} (\frac{1}{2 x})^{7} (- 4)^{4} : \frac{660}{x ^{7}}

化简

\frac{11 !}{5 ! ( 11 - 5 ) !} (\frac{1}{2 x})^{6} (- 4)^{5} : - \frac{7392}{x ^{6}}

化简

\frac{11 !}{6 ! ( 11 - 6 ) !} (\frac{1}{2 x})^{5} (- 4)^{6} : \frac{59136}{x ^{5}}

化简

\frac{11 !}{7 ! ( 11 - 7 ) !} (\frac{1}{2 x})^{4} (- 4)^{7} : - \frac{337920}{x ^{4}}

化简

\frac{11 !}{8 ! ( 11 - 8 ) !} (\frac{1}{2 x})^{3} (- 4)^{8} : \frac{1351680}{x ^{3}}

化简

\frac{11 !}{9 ! ( 11 - 9 ) !} (\frac{1}{2 x})^{2} (- 4)^{9} : - \frac{3604480}{x ^{2}}

化简

\frac{11 !}{10 ! ( 11 - 10 ) !} (\frac{1}{2 x})^{1} (- 4)^{10} : \frac{5767168}{x}

化简

\frac{11 !}{11 ! ( 11 - 11 ) !} (\frac{1}{2 x})^{0} (- 4)^{11} : - 4194304

= \frac{1}{2048 x ^{11}} - \frac{11}{256 x ^{10}} + \frac{55}{32 x ^{9}} - \frac{165}{4 x ^{8}} + \frac{660}{x ^{7}} - \frac{7392}{x ^{6}} + \frac{59136}{x ^{5}} - \frac{337920}{x ^{4}} + \frac{1351680}{x ^{3}} - \frac{3604480}{x ^{2}} + \frac{5767168}{x} - 4194304

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