展开 ((2s^2-1)^2)/(s^6)

解答

展开

\frac{( 2 s ^{2} - 1 ) ^{2}}{s ^{6}}

\frac{4}{s ^{2}} - \frac{4}{s ^{4}} + \frac{1}{s ^{6}}

求解步骤

\frac{( 2 s ^{2} - 1 ) ^{2}}{s ^{6}}

(2 s^{2} - 1)^{2} = 4 s^{4} - 4 s^{2} + 1

= \frac{4 s ^{4} - 4 s ^{2} + 1}{s ^{6}}

使用分式法则:

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

\frac{4 s ^{4} - 4 s ^{2} + 1}{s ^{6}} = \frac{4 s ^{4}}{s ^{6}} - \frac{4 s ^{2}}{s ^{6}} + \frac{1}{s ^{6}}

= \frac{4 s ^{4}}{s ^{6}} - \frac{4 s ^{2}}{s ^{6}} + \frac{1}{s ^{6}}

消掉

\frac{4 s ^{4}}{s ^{6}} : \frac{4}{s ^{2}}

= \frac{4}{s ^{2}} - \frac{4 s ^{2}}{s ^{6}} + \frac{1}{s ^{6}}

消掉

\frac{4 s ^{2}}{s ^{6}} : \frac{4}{s ^{4}}

= \frac{4}{s ^{2}} - \frac{4}{s ^{4}} + \frac{1}{s ^{6}}

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