展开 (2x)^3(x/2-3/(x^3))^6

解答

展开

(2 x)^{3} (\frac{x}{2} - \frac{3}{x ^{3}})^{6}

\frac{x ^{9}}{8} - \frac{9 x ^{5}}{2} + \frac{135 x}{2} - \frac{540}{x ^{3}} + \frac{2430}{x ^{7}} - \frac{5832}{x ^{11}} + \frac{5832}{x ^{15}}

求解步骤

(2 x)^{3} (\frac{x}{2} - \frac{3}{x ^{3}})^{6}

展开

(\frac{x}{2} - \frac{3}{x ^{3}})^{6} : \frac{x ^{6}}{64} - \frac{9 x ^{2}}{16} + \frac{135}{16 x ^{2}} - \frac{135}{2 x ^{6}} + \frac{1215}{4 x ^{10}} - \frac{729}{x ^{14}} + \frac{729}{x ^{18}}

= (2 x)^{3} (\frac{x ^{6}}{64} - \frac{9 x ^{2}}{16} + \frac{135}{16 x ^{2}} - \frac{135}{2 x ^{6}} + \frac{1215}{4 x ^{10}} - \frac{729}{x ^{14}} + \frac{729}{x ^{18}})

打开括号

= (2 x)^{3} \frac{x ^{6}}{64} + (2 x)^{3} (- \frac{9 x ^{2}}{16}) + (2 x)^{3} \frac{135}{16 x ^{2}} + (2 x)^{3} (- \frac{135}{2 x ^{6}}) + (2 x)^{3} \frac{1215}{4 x ^{10}} + (2 x)^{3} (- \frac{729}{x ^{14}}) + (2 x)^{3} \frac{729}{x ^{18}}

化简

(2 x)^{3} \frac{x ^{6}}{64} + (2 x)^{3} (- \frac{9 x ^{2}}{16}) + (2 x)^{3} \frac{135}{16 x ^{2}} + (2 x)^{3} (- \frac{135}{2 x ^{6}}) + (2 x)^{3} \frac{1215}{4 x ^{10}} + (2 x)^{3} (- \frac{729}{x ^{14}}) + (2 x)^{3} \frac{729}{x ^{18}} : \frac{x ^{9}}{8} - \frac{9 x ^{5}}{2} + \frac{135 x}{2} - \frac{540}{x ^{3}} + \frac{2430}{x ^{7}} - \frac{5832}{x ^{11}} + \frac{5832}{x ^{15}}

= \frac{x ^{9}}{8} - \frac{9 x ^{5}}{2} + \frac{135 x}{2} - \frac{540}{x ^{3}} + \frac{2430}{x ^{7}} - \frac{5832}{x ^{11}} + \frac{5832}{x ^{15}}

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