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受欢迎的代数 >

展开 (x^3-2/(x^2))^{10}

解答

展开

(x^{3} - \frac{2}{x ^{2}})^{10}

解答

x^{30} - 20 x^{25} + 180 x^{20} - 960 x^{15} + 3360 x^{10} - 8064 x^{5} + 13440 - \frac{15360}{x ^{5}} + \frac{11520}{x ^{10}} - \frac{5120}{x ^{15}} + \frac{1024}{x ^{20}}

求解步骤

(x^{3} - \frac{2}{x ^{2}})^{10}

使用二项式定理:

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

a = x^{3}, b = - \frac{2}{x ^{2}}

= i = 0 \sum 10 (i 10) (x^{3})^{(10 - i)} (- \frac{2}{x ^{2}})^{i}

展开求和

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

化简

\frac{10 !}{0 ! ( 10 - 0 ) !} (x^{3})^{10} (- \frac{2}{x ^{2}})^{0} : x^{30}

化简

\frac{10 !}{1 ! ( 10 - 1 ) !} (x^{3})^{9} (- \frac{2}{x ^{2}})^{1} : - 20 x^{25}

化简

\frac{10 !}{2 ! ( 10 - 2 ) !} (x^{3})^{8} (- \frac{2}{x ^{2}})^{2} : 180 x^{20}

化简

\frac{10 !}{3 ! ( 10 - 3 ) !} (x^{3})^{7} (- \frac{2}{x ^{2}})^{3} : - 960 x^{15}

化简

\frac{10 !}{4 ! ( 10 - 4 ) !} (x^{3})^{6} (- \frac{2}{x ^{2}})^{4} : 3360 x^{10}

化简

\frac{10 !}{5 ! ( 10 - 5 ) !} (x^{3})^{5} (- \frac{2}{x ^{2}})^{5} : - 8064 x^{5}

化简

\frac{10 !}{6 ! ( 10 - 6 ) !} (x^{3})^{4} (- \frac{2}{x ^{2}})^{6} : 13440

化简

\frac{10 !}{7 ! ( 10 - 7 ) !} (x^{3})^{3} (- \frac{2}{x ^{2}})^{7} : - \frac{15360}{x ^{5}}

化简

\frac{10 !}{8 ! ( 10 - 8 ) !} (x^{3})^{2} (- \frac{2}{x ^{2}})^{8} : \frac{11520}{x ^{10}}

化简

\frac{10 !}{9 ! ( 10 - 9 ) !} (x^{3})^{1} (- \frac{2}{x ^{2}})^{9} : - \frac{5120}{x ^{15}}

化简

\frac{10 !}{10 ! ( 10 - 10 ) !} (x^{3})^{0} (- \frac{2}{x ^{2}})^{10} : \frac{1024}{x ^{20}}

= x^{30} - 20 x^{25} + 180 x^{20} - 960 x^{15} + 3360 x^{10} - 8064 x^{5} + 13440 - \frac{15360}{x ^{5}} + \frac{11520}{x ^{10}} - \frac{5120}{x ^{15}} + \frac{1024}{x ^{20}}

流行的例子

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