erweitern (x(x-1)(x-3)(x-12)(x-23)(x-24))/(40824)

Lösung

erweitern

\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}

Schritte zur Lösung

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

Multipliziere aus

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}

Wende Bruchregel an:

\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}

s im pl i f y (x + 1) (2 x + 1)

e x p an d \frac{x ^{2} - 12 x - 6}{x ^{2} ( x + 1 ) ^{2}}

e x p an d C (- 4, - 2)

e x p an d \frac{x + 1}{2 ^{2 x - 2} ( x ^{2} + 1 )}

e x p an d (- 4 - 107) (3 + 11)