展开 ((8x^6-9)^2)/(576x^6)

解答

展开

\frac{( 8 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

\frac{x ^{6}}{9} - \frac{1}{4} + \frac{9}{64 x ^{6}}

求解步骤

\frac{( 8 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

(8 x^{6} - 9)^{2} = 64 x^{12} - 144 x^{6} + 81

= \frac{64 x ^{12} - 144 x ^{6} + 81}{576 x ^{6}}

使用分式法则:

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

\frac{64 x ^{12} - 144 x ^{6} + 81}{576 x ^{6}} = \frac{64 x ^{12}}{576 x ^{6}} - \frac{144 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

= \frac{64 x ^{12}}{576 x ^{6}} - \frac{144 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

消掉

\frac{64 x ^{12}}{576 x ^{6}} : \frac{x ^{6}}{9}

= \frac{x ^{6}}{9} - \frac{144 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

消掉

\frac{144 x ^{6}}{576 x ^{6}} : \frac{1}{4}

= \frac{x ^{6}}{9} - \frac{1}{4} + \frac{81}{576 x ^{6}}

消掉

\frac{81}{576 x ^{6}} : \frac{9}{64 x ^{6}}

= \frac{x ^{6}}{9} - \frac{1}{4} + \frac{9}{64 x ^{6}}

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