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受欢迎的代数 >

展开 (2x^2-1/x)^8

解答

展开

(2 x^{2} - \frac{1}{x})^{8}

解答

256 x^{16} - 1024 x^{13} + 1792 x^{10} - 1792 x^{7} + 1120 x^{4} - 448 x + \frac{112}{x ^{2}} - \frac{16}{x ^{5}} + \frac{1}{x ^{8}}

求解步骤

(2 x^{2} - \frac{1}{x})^{8}

使用二项式定理:

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

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

= i = 0 \sum 8 (i 8) (2 x^{2})^{(8 - i)} (- \frac{1}{x})^{i}

展开求和

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

化简

\frac{8 !}{0 ! ( 8 - 0 ) !} (2 x^{2})^{8} (- \frac{1}{x})^{0} : 256 x^{16}

化简

\frac{8 !}{1 ! ( 8 - 1 ) !} (2 x^{2})^{7} (- \frac{1}{x})^{1} : - 1024 x^{13}

化简

\frac{8 !}{2 ! ( 8 - 2 ) !} (2 x^{2})^{6} (- \frac{1}{x})^{2} : 1792 x^{10}

化简

\frac{8 !}{3 ! ( 8 - 3 ) !} (2 x^{2})^{5} (- \frac{1}{x})^{3} : - 1792 x^{7}

化简

\frac{8 !}{4 ! ( 8 - 4 ) !} (2 x^{2})^{4} (- \frac{1}{x})^{4} : 1120 x^{4}

化简

\frac{8 !}{5 ! ( 8 - 5 ) !} (2 x^{2})^{3} (- \frac{1}{x})^{5} : - 448 x

化简

\frac{8 !}{6 ! ( 8 - 6 ) !} (2 x^{2})^{2} (- \frac{1}{x})^{6} : \frac{112}{x ^{2}}

化简

\frac{8 !}{7 ! ( 8 - 7 ) !} (2 x^{2})^{1} (- \frac{1}{x})^{7} : - \frac{16}{x ^{5}}

化简

\frac{8 !}{8 ! ( 8 - 8 ) !} (2 x^{2})^{0} (- \frac{1}{x})^{8} : \frac{1}{x ^{8}}

= 256 x^{16} - 1024 x^{13} + 1792 x^{10} - 1792 x^{7} + 1120 x^{4} - 448 x + \frac{112}{x ^{2}} - \frac{16}{x ^{5}} + \frac{1}{x ^{8}}

流行的例子

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