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

Lösung

erweitern

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

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

Schritte zur Lösung

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

(x^{2} + 2)^{3} = x^{6} + 6 x^{4} + 12 x^{2} + 8

= \frac{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}{6}

Wende Bruchregel an:

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

\frac{x ^{6} + 6 x ^{4} + 12 x ^{2} + 8}{6} = \frac{x ^{6}}{6} + \frac{6 x ^{4}}{6} + \frac{12 x ^{2}}{6} + \frac{8}{6}

= \frac{x ^{6}}{6} + \frac{6 x ^{4}}{6} + \frac{12 x ^{2}}{6} + \frac{8}{6}

Teile die Zahlen:

\frac{6}{6} = 1

= \frac{x ^{6}}{6} + x^{4} + \frac{12 x ^{2}}{6} + \frac{8}{6}

Teile die Zahlen:

\frac{12}{6} = 2

= \frac{x ^{6}}{6} + x^{4} + 2 x^{2} + \frac{8}{6}

Streiche

\frac{8}{6} : \frac{4}{3}

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

e x p an d δ (x) \cdot (x - 1)

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

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

e x p an d \frac{6}{( 1 + 5.1 s ) ( 1 + 0.1 s )}

e x p an d (3 x^{2} + 2) e^{x} + (x^{3} + 2 x) e^{x}