erweitern ((x-0)(x-1)(x-2)(x-6))/(-60)

Lösung

erweitern

\frac{( x - 0 ) ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

- \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{x}{5}

Schritte zur Lösung

\frac{( x - 0 ) ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

x - 0 = x

= \frac{x ( x - 1 ) ( x - 2 ) ( x - 6 )}{- 60}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x ( x - 1 ) ( x - 2 ) ( x - 6 )}{60}

Multipliziere aus

x (x - 1) (x - 2) (x - 6) : x^{4} - 9 x^{3} + 20 x^{2} - 12 x

= - \frac{x ^{4} - 9 x ^{3} + 20 x ^{2} - 12 x}{60}

Wende Bruchregel an:

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

\frac{x ^{4} - 9 x ^{3} + 20 x ^{2} - 12 x}{60} = - (\frac{x ^{4}}{60}) - (- \frac{9 x ^{3}}{60}) - (\frac{20 x ^{2}}{60}) - (- \frac{12 x}{60})

= - (\frac{x ^{4}}{60}) - (- \frac{9 x ^{3}}{60}) - (\frac{20 x ^{2}}{60}) - (- \frac{12 x}{60})

Entferne die Klammern:

(a) = a, - (- a) = a

= - \frac{x ^{4}}{60} + \frac{9 x ^{3}}{60} - \frac{20 x ^{2}}{60} + \frac{12 x}{60}

Streiche

\frac{9 x ^{3}}{60} : \frac{3 x ^{3}}{20}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{20 x ^{2}}{60} + \frac{12 x}{60}

Streiche

\frac{20 x ^{2}}{60} : \frac{x ^{2}}{3}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{12 x}{60}

Streiche

\frac{12 x}{60} : \frac{x}{5}

= - \frac{x ^{4}}{60} + \frac{3 x ^{3}}{20} - \frac{x ^{2}}{3} + \frac{x}{5}

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

e x p an d 2 (3 x - 2 = 2)

e x p an d (\frac{2 + x}{( 10 x ^{2} - 1 )}) (1000 x^{6} - 1)

e x p an d \frac{48 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}}

e x p an d (sin (2 x) + 1)^{2}