erweitern (k(k+1)(2k+7))/6

Lösung

erweitern

\frac{k ( k + 1 ) ( 2 k + 7 )}{6}

\frac{k ^{3}}{3} + \frac{3 k ^{2}}{2} + \frac{7 k}{6}

Schritte zur Lösung

\frac{k ( k + 1 ) ( 2 k + 7 )}{6}

Multipliziere aus

k (k + 1) (2 k + 7) : 2 k^{3} + 9 k^{2} + 7 k

= \frac{2 k ^{3} + 9 k ^{2} + 7 k}{6}

Wende Bruchregel an:

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

\frac{2 k ^{3} + 9 k ^{2} + 7 k}{6} = \frac{2 k ^{3}}{6} + \frac{9 k ^{2}}{6} + \frac{7 k}{6}

= \frac{2 k ^{3}}{6} + \frac{9 k ^{2}}{6} + \frac{7 k}{6}

Streiche

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

= \frac{k ^{3}}{3} + \frac{9 k ^{2}}{6} + \frac{7 k}{6}

Streiche

\frac{9 k ^{2}}{6} : \frac{3 k ^{2}}{2}

= \frac{k ^{3}}{3} + \frac{3 k ^{2}}{2} + \frac{7 k}{6}

e x p an d \frac{2 a ^{2}}{a}

e x p an d \frac{( a + h ) ^{4}}{2}

e x p an d 2 (y (y - 2))

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

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