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

Lösung

erweitern

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

\frac{k ^{3}}{3} + \frac{k ^{2}}{2} + \frac{7 k}{6} + 1

Schritte zur Lösung

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

Multipliziere aus

(k + 1) (2 k^{2} + k + 6) : 2 k^{3} + 3 k^{2} + 7 k + 6

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

Wende Bruchregel an:

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

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

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

Wende Regel an

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 k ^{3}}{6} + \frac{3 k ^{2}}{6} + \frac{7 k}{6} + 1

Streiche

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

= \frac{k ^{3}}{3} + \frac{3 k ^{2}}{6} + \frac{7 k}{6} + 1

Streiche

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

= \frac{k ^{3}}{3} + \frac{k ^{2}}{2} + \frac{7 k}{6} + 1

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