erweitern (k(k+1)(k+2)(k+3))/4

Lösung

erweitern

\frac{k ( k + 1 ) ( k + 2 ) ( k + 3 )}{4}

\frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{11 k ^{2}}{4} + \frac{3 k}{2}

Schritte zur Lösung

\frac{k ( k + 1 ) ( k + 2 ) ( k + 3 )}{4}

Multipliziere aus

k (k + 1) (k + 2) (k + 3) : k^{4} + 6 k^{3} + 11 k^{2} + 6 k

= \frac{k ^{4} + 6 k ^{3} + 11 k ^{2} + 6 k}{4}

Wende Bruchregel an:

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

\frac{k ^{4} + 6 k ^{3} + 11 k ^{2} + 6 k}{4} = \frac{k ^{4}}{4} + \frac{6 k ^{3}}{4} + \frac{11 k ^{2}}{4} + \frac{6 k}{4}

= \frac{k ^{4}}{4} + \frac{6 k ^{3}}{4} + \frac{11 k ^{2}}{4} + \frac{6 k}{4}

Streiche

\frac{6 k ^{3}}{4} : \frac{3 k ^{3}}{2}

= \frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{11 k ^{2}}{4} + \frac{6 k}{4}

Streiche

\frac{6 k}{4} : \frac{3 k}{2}

= \frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{11 k ^{2}}{4} + \frac{3 k}{2}

e x p an d (1 + tan (x)) tan (2 x)

e x p an d (e + 3) (e - 5)

s im pl i f y (5 - x) (x - \frac{x}{2})

e x p an d (2 x + 2) l e f t (3 x - 1)

s im pl i f y (1 + \frac{x}{1 - x}) \cdot (1 - \frac{x}{1 + x})