erweitern ((-2x^3+1)^9)/(x^{21)}

Lösung

erweitern

\frac{( - 2 x ^{3} + 1 ) ^{9}}{x ^{21}}

- 512 x^{6} + 2304 x^{3} - 4608 + \frac{5376}{x ^{3}} - \frac{4032}{x ^{6}} + \frac{2016}{x ^{9}} - \frac{672}{x ^{12}} + \frac{144}{x ^{15}} - \frac{18}{x ^{18}} + \frac{1}{x ^{21}}

Schritte zur Lösung

\frac{( - 2 x ^{3} + 1 ) ^{9}}{x ^{21}}

(- 2 x^{3} + 1)^{9} = - 512 x^{27} + 2304 x^{24} - 4608 x^{21} + 5376 x^{18} - 4032 x^{15} + 2016 x^{12} - 672 x^{9} + 144 x^{6} - 18 x^{3} + 1

= \frac{( - 512 x ^{27} + 2304 x ^{24} - 4608 x ^{21} + 5376 x ^{18} - 4032 x ^{15} + 2016 x ^{12} - 672 x ^{9} + 144 x ^{6} - 18 x ^{3} + 1 )}{x ^{21}}

Entferne die Klammern:

(- a) = - a

= \frac{- 512 x ^{27} + 2304 x ^{24} - 4608 x ^{21} + 5376 x ^{18} - 4032 x ^{15} + 2016 x ^{12} - 672 x ^{9} + 144 x ^{6} - 18 x ^{3} + 1}{x ^{21}}

Wende Bruchregel an:

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

\frac{- 512 x ^{27} + 2304 x ^{24} - 4608 x ^{21} + 5376 x ^{18} - 4032 x ^{15} + 2016 x ^{12} - 672 x ^{9} + 144 x ^{6} - 18 x ^{3} + 1}{x ^{21}} = - \frac{512 x ^{27}}{x ^{21}} + \frac{2304 x ^{24}}{x ^{21}} - \frac{4608 x ^{21}}{x ^{21}} + \frac{5376 x ^{18}}{x ^{21}} - \frac{4032 x ^{15}}{x ^{21}} + \frac{2016 x ^{12}}{x ^{21}} - \frac{672 x ^{9}}{x ^{21}} + \frac{144 x ^{6}}{x ^{21}} - \frac{18 x ^{3}}{x ^{21}} + \frac{1}{x ^{21}}

= - \frac{512 x ^{27}}{x ^{21}} + \frac{2304 x ^{24}}{x ^{21}} - \frac{4608 x ^{21}}{x ^{21}} + \frac{5376 x ^{18}}{x ^{21}} - \frac{4032 x ^{15}}{x ^{21}} + \frac{2016 x ^{12}}{x ^{21}} - \frac{672 x ^{9}}{x ^{21}} + \frac{144 x ^{6}}{x ^{21}} - \frac{18 x ^{3}}{x ^{21}} + \frac{1}{x ^{21}}

\frac{512 x ^{27}}{x ^{21}} = 512 x^{6}

\frac{2304 x ^{24}}{x ^{21}} = 2304 x^{3}

\frac{4608 x ^{21}}{x ^{21}} = 4608

\frac{5376 x ^{18}}{x ^{21}} = \frac{5376}{x ^{3}}

\frac{4032 x ^{15}}{x ^{21}} = \frac{4032}{x ^{6}}

\frac{2016 x ^{12}}{x ^{21}} = \frac{2016}{x ^{9}}

\frac{672 x ^{9}}{x ^{21}} = \frac{672}{x ^{12}}

\frac{144 x ^{6}}{x ^{21}} = \frac{144}{x ^{15}}

\frac{18 x ^{3}}{x ^{21}} = \frac{18}{x ^{18}}

= - 512 x^{6} + 2304 x^{3} - 4608 + \frac{5376}{x ^{3}} - \frac{4032}{x ^{6}} + \frac{2016}{x ^{9}} - \frac{672}{x ^{12}} + \frac{144}{x ^{15}} - \frac{18}{x ^{18}} + \frac{1}{x ^{21}}

s im pl i f y 2 (3 + 4)

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

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

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

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