展開する (x(x-1)(x-3)(x-12)(x-23)(x-24))/(40824)

解

展開する

\frac{x ( x - 1 ) ( x - 3 ) ( x - 12 ) ( x - 23 ) ( x - 24 )}{40824}

\frac{x ^{6}}{40824} - \frac{x ^{5}}{648} + \frac{1355 x ^{4}}{40824} - \frac{3755 x ^{3}}{13608} + \frac{829 x ^{2}}{1134} - \frac{92 x}{189}

解答ステップ

\frac{x ( x - 1 ) ( x - 3 ) ( x - 12 ) ( x - 23 ) ( x - 24 )}{40824}

拡張

x (x - 1) (x - 3) (x - 12) (x - 23) (x - 24) : x^{6} - 63 x^{5} + 1355 x^{4} - 11265 x^{3} + 29844 x^{2} - 19872 x

= \frac{x ^{6} - 63 x ^{5} + 1355 x ^{4} - 11265 x ^{3} + 29844 x ^{2} - 19872 x}{40824}

分数の規則を適用する:

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

\frac{x ^{6} - 63 x ^{5} + 1355 x ^{4} - 11265 x ^{3} + 29844 x ^{2} - 19872 x}{40824} = \frac{x ^{6}}{40824} - \frac{63 x ^{5}}{40824} + \frac{1355 x ^{4}}{40824} - \frac{11265 x ^{3}}{40824} + \frac{29844 x ^{2}}{40824} - \frac{19872 x}{40824}

= \frac{x ^{6}}{40824} - \frac{63 x ^{5}}{40824} + \frac{1355 x ^{4}}{40824} - \frac{11265 x ^{3}}{40824} + \frac{29844 x ^{2}}{40824} - \frac{19872 x}{40824}

\frac{63 x ^{5}}{40824} = \frac{x ^{5}}{648}

\frac{11265 x ^{3}}{40824} = \frac{3755 x ^{3}}{13608}

\frac{29844 x ^{2}}{40824} = \frac{829 x ^{2}}{1134}

\frac{19872 x}{40824} = \frac{92 x}{189}

= \frac{x ^{6}}{40824} - \frac{x ^{5}}{648} + \frac{1355 x ^{4}}{40824} - \frac{3755 x ^{3}}{13608} + \frac{829 x ^{2}}{1134} - \frac{92 x}{189}