erweitern ((12-x^2)^2)/9

Lösung

erweitern

\frac{( 12 - x ^{2} ) ^{2}}{9}

\frac{x ^{4}}{9} - \frac{8 x ^{2}}{3} + 16

Schritte zur Lösung

\frac{( 12 - x ^{2} ) ^{2}}{9}

(12 - x^{2})^{2} = 144 - 24 x^{2} + x^{4}

= \frac{144 - 24 x ^{2} + x ^{4}}{9}

Wende Bruchregel an:

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

\frac{144 - 24 x ^{2} + x ^{4}}{9} = \frac{144}{9} - \frac{24 x ^{2}}{9} + \frac{x ^{4}}{9}

= \frac{144}{9} - \frac{24 x ^{2}}{9} + \frac{x ^{4}}{9}

Teile die Zahlen:

\frac{144}{9} = 16

= 16 - \frac{24 x ^{2}}{9} + \frac{x ^{4}}{9}

Streiche

\frac{24 x ^{2}}{9} : \frac{8 x ^{2}}{3}

= 16 - \frac{8 x ^{2}}{3} + \frac{x ^{4}}{9}

Rewrite in standard form

= \frac{x ^{4}}{9} - \frac{8 x ^{2}}{3} + 16

e x p an d (1 + \frac{1}{2} x)^{6}

e x p an d x^{\frac{2}{3}} (5 - 2 x)

s im pl i f y (b a x - a b c)^{2}

e x p an d f oco (4, - 3)

e x p an d \frac{6 x ^{2} - 2}{( x ^{2} + 1 ) ^{3}}