erweitern ((x^4+3)^3)/(12)

Lösung

erweitern

\frac{( x ^{4} + 3 ) ^{3}}{12}

\frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{9}{4}

Schritte zur Lösung

\frac{( x ^{4} + 3 ) ^{3}}{12}

(x^{4} + 3)^{3} = x^{12} + 9 x^{8} + 27 x^{4} + 27

= \frac{x ^{12} + 9 x ^{8} + 27 x ^{4} + 27}{12}

Wende Bruchregel an:

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

\frac{x ^{12} + 9 x ^{8} + 27 x ^{4} + 27}{12} = \frac{x ^{12}}{12} + \frac{9 x ^{8}}{12} + \frac{27 x ^{4}}{12} + \frac{27}{12}

= \frac{x ^{12}}{12} + \frac{9 x ^{8}}{12} + \frac{27 x ^{4}}{12} + \frac{27}{12}

Streiche

\frac{9 x ^{8}}{12} : \frac{3 x ^{8}}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{27 x ^{4}}{12} + \frac{27}{12}

Streiche

\frac{27 x ^{4}}{12} : \frac{9 x ^{4}}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{27}{12}

Streiche

\frac{27}{12} : \frac{9}{4}

= \frac{x ^{12}}{12} + \frac{3 x ^{8}}{4} + \frac{9 x ^{4}}{4} + \frac{9}{4}

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

e x p an d 2 (e^{s i n (\frac{x}{4})} - 1)

e x p an d x (3 x + 5 vx) (v + x \frac{d v}{d x})

e x p an d (5 e^{3} + 3 p^{2})^{6}

e x p an d e^{12 x} (6 x^{2} + 2 x)