展开 ((x^2-1)^4)/4

解答

展开

\frac{( x ^{2} - 1 ) ^{4}}{4}

\frac{x ^{8}}{4} - x^{6} + \frac{3 x ^{4}}{2} - x^{2} + \frac{1}{4}

求解步骤

\frac{( x ^{2} - 1 ) ^{4}}{4}

(x^{2} - 1)^{4} = x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1

= \frac{x ^{8} - 4 x ^{6} + 6 x ^{4} - 4 x ^{2} + 1}{4}

使用分式法则:

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

\frac{x ^{8} - 4 x ^{6} + 6 x ^{4} - 4 x ^{2} + 1}{4} = \frac{x ^{8}}{4} - \frac{4 x ^{6}}{4} + \frac{6 x ^{4}}{4} - \frac{4 x ^{2}}{4} + \frac{1}{4}

= \frac{x ^{8}}{4} - \frac{4 x ^{6}}{4} + \frac{6 x ^{4}}{4} - \frac{4 x ^{2}}{4} + \frac{1}{4}

数字相除:

\frac{4}{4} = 1

= \frac{x ^{8}}{4} - x^{6} + \frac{6 x ^{4}}{4} - \frac{4 x ^{2}}{4} + \frac{1}{4}

消掉

\frac{6 x ^{4}}{4} : \frac{3 x ^{4}}{2}

= \frac{x ^{8}}{4} - x^{6} + \frac{3 x ^{4}}{2} - \frac{4 x ^{2}}{4} + \frac{1}{4}

数字相除:

\frac{4}{4} = 1

= \frac{x ^{8}}{4} - x^{6} + \frac{3 x ^{4}}{2} - x^{2} + \frac{1}{4}

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