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 \frac{π ( e ^{3} - 1 )}{3 e ^{3}}

e x p an d (4 a^{2} - 3 b + 2 c d - 5 e)^{2}

e x p an d (2 x^{3} - 4 x^{2} + 1)^{5}

e x p an d π (4 x - 3)^{2}

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