erweitern ((x-4)(x-12)(x-20)(x-24))/(4608)

Lösung

erweitern

\frac{( x - 4 ) ( x - 12 ) ( x - 20 ) ( x - 24 )}{4608}

\frac{x ^{4}}{4608} - \frac{5 x ^{3}}{384} + \frac{77 x ^{2}}{288} - \frac{17 x}{8} + 5

Schritte zur Lösung

\frac{( x - 4 ) ( x - 12 ) ( x - 20 ) ( x - 24 )}{4608}

Multipliziere aus

(x - 4) (x - 12) (x - 20) (x - 24) : x^{4} - 60 x^{3} + 1232 x^{2} - 9792 x + 23040

= \frac{x ^{4} - 60 x ^{3} + 1232 x ^{2} - 9792 x + 23040}{4608}

Wende Bruchregel an:

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

\frac{x ^{4} - 60 x ^{3} + 1232 x ^{2} - 9792 x + 23040}{4608} = \frac{x ^{4}}{4608} - \frac{60 x ^{3}}{4608} + \frac{1232 x ^{2}}{4608} - \frac{9792 x}{4608} + \frac{23040}{4608}

= \frac{x ^{4}}{4608} - \frac{60 x ^{3}}{4608} + \frac{1232 x ^{2}}{4608} - \frac{9792 x}{4608} + \frac{23040}{4608}

\frac{60 x ^{3}}{4608} = \frac{5 x ^{3}}{384}

\frac{1232 x ^{2}}{4608} = \frac{77 x ^{2}}{288}

\frac{9792 x}{4608} = \frac{17 x}{8}

\frac{23040}{4608} = 5

= \frac{x ^{4}}{4608} - \frac{5 x ^{3}}{384} + \frac{77 x ^{2}}{288} - \frac{17 x}{8} + 5

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