erweitern ((x+1)(x+2)(2x+3))/6

Lösung

erweitern

\frac{( x + 1 ) ( x + 2 ) ( 2 x + 3 )}{6}

\frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} + \frac{13 x}{6} + 1

Schritte zur Lösung

\frac{( x + 1 ) ( x + 2 ) ( 2 x + 3 )}{6}

Multipliziere aus

(x + 1) (x + 2) (2 x + 3) : 2 x^{3} + 9 x^{2} + 13 x + 6

= \frac{2 x ^{3} + 9 x ^{2} + 13 x + 6}{6}

Wende Bruchregel an:

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

\frac{2 x ^{3} + 9 x ^{2} + 13 x + 6}{6} = \frac{2 x ^{3}}{6} + \frac{9 x ^{2}}{6} + \frac{13 x}{6} + \frac{6}{6}

= \frac{2 x ^{3}}{6} + \frac{9 x ^{2}}{6} + \frac{13 x}{6} + \frac{6}{6}

Wende Regel an

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 x ^{3}}{6} + \frac{9 x ^{2}}{6} + \frac{13 x}{6} + 1

Streiche

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

= \frac{x ^{3}}{3} + \frac{9 x ^{2}}{6} + \frac{13 x}{6} + 1

Streiche

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

= \frac{x ^{3}}{3} + \frac{3 x ^{2}}{2} + \frac{13 x}{6} + 1

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

e x p an d (sec (x) +, - 1) (sec (x) -, + 1)

e x p an d \frac{x ^{4} ( 16 x ^{2} y ^{6} + 3 ) ^{2}}{16}

e x p an d 38

\frac{d}{d t} ((z (t, x, y)) (x^{2} + y^{2}))