erweitern ((x^2+1)^4)/8

Lösung

erweitern

\frac{( x ^{2} + 1 ) ^{4}}{8}

\frac{x ^{8}}{8} + \frac{x ^{6}}{2} + \frac{3 x ^{4}}{4} + \frac{x ^{2}}{2} + \frac{1}{8}

Schritte zur Lösung

\frac{( x ^{2} + 1 ) ^{4}}{8}

(x^{2} + 1)^{4} = x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 1

= \frac{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1}{8}

Wende Bruchregel an:

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

\frac{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1}{8} = \frac{x ^{8}}{8} + \frac{4 x ^{6}}{8} + \frac{6 x ^{4}}{8} + \frac{4 x ^{2}}{8} + \frac{1}{8}

= \frac{x ^{8}}{8} + \frac{4 x ^{6}}{8} + \frac{6 x ^{4}}{8} + \frac{4 x ^{2}}{8} + \frac{1}{8}

Streiche

\frac{4 x ^{6}}{8} : \frac{x ^{6}}{2}

= \frac{x ^{8}}{8} + \frac{x ^{6}}{2} + \frac{6 x ^{4}}{8} + \frac{4 x ^{2}}{8} + \frac{1}{8}

Streiche

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

= \frac{x ^{8}}{8} + \frac{x ^{6}}{2} + \frac{3 x ^{4}}{4} + \frac{4 x ^{2}}{8} + \frac{1}{8}

Streiche

\frac{4 x ^{2}}{8} : \frac{x ^{2}}{2}

= \frac{x ^{8}}{8} + \frac{x ^{6}}{2} + \frac{3 x ^{4}}{4} + \frac{x ^{2}}{2} + \frac{1}{8}

s im pl i f y (x + 6 - 3) (x + 6 + 3)

e x p an d (\frac{4}{x} - \frac{1}{x ^{3}})^{2}

e x p an d (\frac{1}{20} e^{\frac{x}{20}} - \frac{1}{20} e^{- \frac{x}{20}})^{2}

e x p an d A (- 2, - 3) B (x_{2}, 2)

s im pl i f y (I - E D) (I + \frac{E D}{I - D E})