展開する (x(x-1)(x-12)(x-21)(x-23)(x-24))/(40824)

解

展開する

\frac{x ( x - 1 ) ( x - 12 ) ( x - 21 ) ( x - 23 ) ( x - 24 )}{40824}

\frac{x ^{6}}{40824} - \frac{x ^{5}}{504} + \frac{2435 x ^{4}}{40824} - \frac{10805 x ^{3}}{13608} + \frac{4699 x ^{2}}{1134} - \frac{92 x}{27}

解答ステップ

\frac{x ( x - 1 ) ( x - 12 ) ( x - 21 ) ( x - 23 ) ( x - 24 )}{40824}

拡張

x (x - 1) (x - 12) (x - 21) (x - 23) (x - 24) : x^{6} - 81 x^{5} + 2435 x^{4} - 32415 x^{3} + 169164 x^{2} - 139104 x

= \frac{x ^{6} - 81 x ^{5} + 2435 x ^{4} - 32415 x ^{3} + 169164 x ^{2} - 139104 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} - 81 x ^{5} + 2435 x ^{4} - 32415 x ^{3} + 169164 x ^{2} - 139104 x}{40824} = \frac{x ^{6}}{40824} - \frac{81 x ^{5}}{40824} + \frac{2435 x ^{4}}{40824} - \frac{32415 x ^{3}}{40824} + \frac{169164 x ^{2}}{40824} - \frac{139104 x}{40824}

= \frac{x ^{6}}{40824} - \frac{81 x ^{5}}{40824} + \frac{2435 x ^{4}}{40824} - \frac{32415 x ^{3}}{40824} + \frac{169164 x ^{2}}{40824} - \frac{139104 x}{40824}

\frac{81 x ^{5}}{40824} = \frac{x ^{5}}{504}

\frac{32415 x ^{3}}{40824} = \frac{10805 x ^{3}}{13608}

\frac{169164 x ^{2}}{40824} = \frac{4699 x ^{2}}{1134}

\frac{139104 x}{40824} = \frac{92 x}{27}

= \frac{x ^{6}}{40824} - \frac{x ^{5}}{504} + \frac{2435 x ^{4}}{40824} - \frac{10805 x ^{3}}{13608} + \frac{4699 x ^{2}}{1134} - \frac{92 x}{27}