erweitern (ir(2+x^2)^3)/8

Lösung

erweitern

\frac{i r ( 2 + x ^{2} ) ^{3}}{8}

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

Schritte zur Lösung

\frac{i r ( 2 + x ^{2} ) ^{3}}{8}

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

= \frac{i r ( x ^{6} + 6 x ^{4} + 12 x ^{2} + 8 )}{8}

Multipliziere aus

i r (8 + 12 x^{2} + 6 x^{4} + x^{6}) : 8 i r + 12 i r x^{2} + 6 i r x^{4} + i r x^{6}

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

Wende Bruchregel an:

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

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

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

Teile die Zahlen:

\frac{8}{8} = 1

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

Streiche

\frac{12 i r x ^{2}}{8} : \frac{3 i r x ^{2}}{2}

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

Streiche

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

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

Schreibe

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

in der Standard komplexen Form um:

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

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

e x p an d \frac{( 2 x - 3 ) ( x + 9 )}{4 x ( 2 x - 9 )}

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

e x p an d A (4, - 1) B (2, 3) C (2, 3)

e x p an d \frac{6 s ^{2} + 50}{( s + 3 ) ( s + 4 )}

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