erweitern (r(r+1)(2r+1))/6

Lösung

erweitern

\frac{r ( r + 1 ) ( 2 r + 1 )}{6}

\frac{r ^{3}}{3} + \frac{r ^{2}}{2} + \frac{r}{6}

Schritte zur Lösung

\frac{r ( r + 1 ) ( 2 r + 1 )}{6}

Multipliziere aus

r (r + 1) (2 r + 1) : 2 r^{3} + 3 r^{2} + r

= \frac{2 r ^{3} + 3 r ^{2} + r}{6}

Wende Bruchregel an:

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

\frac{2 r ^{3} + 3 r ^{2} + r}{6} = \frac{2 r ^{3}}{6} + \frac{3 r ^{2}}{6} + \frac{r}{6}

= \frac{2 r ^{3}}{6} + \frac{3 r ^{2}}{6} + \frac{r}{6}

Streiche

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

= \frac{r ^{3}}{3} + \frac{3 r ^{2}}{6} + \frac{r}{6}

Streiche

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

= \frac{r ^{3}}{3} + \frac{r ^{2}}{2} + \frac{r}{6}

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

e x p an d \frac{( b + c + a ) ( 2 b c + b ^{2} + c ^{2} - a ^{2} )}{2 b c ( b + c - a )}

e x p an d (3 - x)^{5}

\frac{d}{d t} ((x) (a t - a sin (t)))

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