展开 ((2x^3+3)^6)/(x^{12)}

解答

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\frac{( 2 x ^{3} + 3 ) ^{6}}{x ^{12}}

64 x^{6} + 576 x^{3} + 2160 + \frac{4320}{x ^{3}} + \frac{4860}{x ^{6}} + \frac{2916}{x ^{9}} + \frac{729}{x ^{12}}

求解步骤

\frac{( 2 x ^{3} + 3 ) ^{6}}{x ^{12}}

(2 x^{3} + 3)^{6} = 64 x^{18} + 576 x^{15} + 2160 x^{12} + 4320 x^{9} + 4860 x^{6} + 2916 x^{3} + 729

= \frac{64 x ^{18} + 576 x ^{15} + 2160 x ^{12} + 4320 x ^{9} + 4860 x ^{6} + 2916 x ^{3} + 729}{x ^{12}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{64 x ^{18} + 576 x ^{15} + 2160 x ^{12} + 4320 x ^{9} + 4860 x ^{6} + 2916 x ^{3} + 729}{x ^{12}} = \frac{64 x ^{18}}{x ^{12}} + \frac{576 x ^{15}}{x ^{12}} + \frac{2160 x ^{12}}{x ^{12}} + \frac{4320 x ^{9}}{x ^{12}} + \frac{4860 x ^{6}}{x ^{12}} + \frac{2916 x ^{3}}{x ^{12}} + \frac{729}{x ^{12}}

= \frac{64 x ^{18}}{x ^{12}} + \frac{576 x ^{15}}{x ^{12}} + \frac{2160 x ^{12}}{x ^{12}} + \frac{4320 x ^{9}}{x ^{12}} + \frac{4860 x ^{6}}{x ^{12}} + \frac{2916 x ^{3}}{x ^{12}} + \frac{729}{x ^{12}}

\frac{64 x ^{18}}{x ^{12}} = 64 x^{6}

\frac{576 x ^{15}}{x ^{12}} = 576 x^{3}

\frac{2160 x ^{12}}{x ^{12}} = 2160

\frac{4320 x ^{9}}{x ^{12}} = \frac{4320}{x ^{3}}

\frac{4860 x ^{6}}{x ^{12}} = \frac{4860}{x ^{6}}

\frac{2916 x ^{3}}{x ^{12}} = \frac{2916}{x ^{9}}

= 64 x^{6} + 576 x^{3} + 2160 + \frac{4320}{x ^{3}} + \frac{4860}{x ^{6}} + \frac{2916}{x ^{9}} + \frac{729}{x ^{12}}

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