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

Lösung

erweitern

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

\frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{x}{3}

Schritte zur Lösung

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

Multipliziere aus

x (x - 1) (x - 2) : x^{3} - 3 x^{2} + 2 x

= \frac{x ^{3} - 3 x ^{2} + 2 x}{6}

Wende Bruchregel an:

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

\frac{x ^{3} - 3 x ^{2} + 2 x}{6} = \frac{x ^{3}}{6} - \frac{3 x ^{2}}{6} + \frac{2 x}{6}

= \frac{x ^{3}}{6} - \frac{3 x ^{2}}{6} + \frac{2 x}{6}

Streiche

\frac{3 x ^{2}}{6} : \frac{x ^{2}}{2}

= \frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{2 x}{6}

Streiche

\frac{2 x}{6} : \frac{x}{3}

= \frac{x ^{3}}{6} - \frac{x ^{2}}{2} + \frac{x}{3}

e x p an d (e - 5) (f - 2 g)

e x p an d \frac{1 + x - 4 x ^{2}}{( 1 - x ) ^{2} ( 1 + 2 x )}

e x p an d \frac{13 ( x - 1 )}{( 5 - 2 x ) ( 3 x - 1 )}

e x p an d \frac{2 x ^{3} - 1}{( 2 x ^{4} - 4 x ) ^{3}}

e x p an d \frac{( 3 - x ) ^{2}}{9}