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受欢迎的代数 >

展开 (2x-3/(x^2))^9

解答

展开

(2 x - \frac{3}{x ^{2}})^{9}

解答

512 x^{9} - 6912 x^{6} + 41472 x^{3} - 145152 + \frac{326592}{x ^{3}} - \frac{489888}{x ^{6}} + \frac{489888}{x ^{9}} - \frac{314928}{x ^{12}} + \frac{118098}{x ^{15}} - \frac{19683}{x ^{18}}

求解步骤

(2 x - \frac{3}{x ^{2}})^{9}

使用二项式定理:

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

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

= i = 0 \sum 9 (i 9) (2 x)^{(9 - i)} (- \frac{3}{x ^{2}})^{i}

展开求和

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

化简

\frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} (- \frac{3}{x ^{2}})^{0} : 512 x^{9}

化简

\frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} (- \frac{3}{x ^{2}})^{1} : - 6912 x^{6}

化简

\frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} (- \frac{3}{x ^{2}})^{2} : 41472 x^{3}

化简

\frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} (- \frac{3}{x ^{2}})^{3} : - 145152

化简

\frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} (- \frac{3}{x ^{2}})^{4} : \frac{326592}{x ^{3}}

化简

\frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} (- \frac{3}{x ^{2}})^{5} : - \frac{489888}{x ^{6}}

化简

\frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} (- \frac{3}{x ^{2}})^{6} : \frac{489888}{x ^{9}}

化简

\frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} (- \frac{3}{x ^{2}})^{7} : - \frac{314928}{x ^{12}}

化简

\frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} (- \frac{3}{x ^{2}})^{8} : \frac{118098}{x ^{15}}

化简

\frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} (- \frac{3}{x ^{2}})^{9} : - \frac{19683}{x ^{18}}

= 512 x^{9} - 6912 x^{6} + 41472 x^{3} - 145152 + \frac{326592}{x ^{3}} - \frac{489888}{x ^{6}} + \frac{489888}{x ^{9}} - \frac{314928}{x ^{12}} + \frac{118098}{x ^{15}} - \frac{19683}{x ^{18}}

流行的例子

展开 ((-x^2+9))/((x^2+9)^2)

e x p an d \frac{( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

e x p an d csc (0)

展开-e^x(x+5)

e x p an d - e^{x} (x + 5)

展开 ln(\sqrt[3]{x/5})

e x p an d ln (3 \frac{x}{5})

展开 (e^{-s})/(s(s+2))

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