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

Lösung

erweitern

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

\frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + \frac{1}{6}

Schritte zur Lösung

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

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= \frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{6}

Wende Bruchregel an:

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

\frac{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}{6} = \frac{x ^{6}}{6} + \frac{3 x ^{4}}{6} + \frac{3 x ^{2}}{6} + \frac{1}{6}

= \frac{x ^{6}}{6} + \frac{3 x ^{4}}{6} + \frac{3 x ^{2}}{6} + \frac{1}{6}

Streiche

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

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{3 x ^{2}}{6} + \frac{1}{6}

Streiche

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

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + \frac{1}{6}

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

e x p an d - \frac{5 x ( 4 x - 14 )}{3}

e x p an d \frac{3 ( s + x )}{s ( s + 1 )}

e x p an d \frac{10 ( 5 + 74 )}{49}

s im pl i f y e^{(- 2 + i) t}