展开 ((x^4+3)^3)/(12)

解答

展开

\frac{( x ^{4} + 3 ) ^{3}}{12}

\frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{9}{4}

求解步骤

\frac{( x ^{4} + 3 ) ^{3}}{12}

(x^{4} + 3)^{3} = x^{12} + 9 x^{8} + 27 x^{4} + 27

= \frac{x ^{12} + 9 x ^{8} + 27 x ^{4} + 27}{12}

使用分式法则:

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

\frac{x ^{12} + 9 x ^{8} + 27 x ^{4} + 27}{12} = \frac{x ^{12}}{12} + \frac{9 x ^{8}}{12} + \frac{27 x ^{4}}{12} + \frac{27}{12}

= \frac{x ^{12}}{12} + \frac{9 x ^{8}}{12} + \frac{27 x ^{4}}{12} + \frac{27}{12}

消掉

\frac{9 x ^{8}}{12} : \frac{3 x ^{8}}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{27 x ^{4}}{12} + \frac{27}{12}

消掉

\frac{27 x ^{4}}{12} : \frac{9 x ^{4}}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{27}{12}

消掉

\frac{27}{12} : \frac{9}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{9}{4}

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