erweitern ((3x^3+1)^6)/(x^{12)}

Lösung

erweitern

\frac{( 3 x ^{3} + 1 ) ^{6}}{x ^{12}}

729 x^{6} + 1458 x^{3} + 1215 + \frac{540}{x ^{3}} + \frac{135}{x ^{6}} + \frac{18}{x ^{9}} + \frac{1}{x ^{12}}

Schritte zur Lösung

\frac{( 3 x ^{3} + 1 ) ^{6}}{x ^{12}}

(3 x^{3} + 1)^{6} = 729 x^{18} + 1458 x^{15} + 1215 x^{12} + 540 x^{9} + 135 x^{6} + 18 x^{3} + 1

= \frac{729 x ^{18} + 1458 x ^{15} + 1215 x ^{12} + 540 x ^{9} + 135 x ^{6} + 18 x ^{3} + 1}{x ^{12}}

Wende Bruchregel an:

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

\frac{729 x ^{18} + 1458 x ^{15} + 1215 x ^{12} + 540 x ^{9} + 135 x ^{6} + 18 x ^{3} + 1}{x ^{12}} = \frac{729 x ^{18}}{x ^{12}} + \frac{1458 x ^{15}}{x ^{12}} + \frac{1215 x ^{12}}{x ^{12}} + \frac{540 x ^{9}}{x ^{12}} + \frac{135 x ^{6}}{x ^{12}} + \frac{18 x ^{3}}{x ^{12}} + \frac{1}{x ^{12}}

= \frac{729 x ^{18}}{x ^{12}} + \frac{1458 x ^{15}}{x ^{12}} + \frac{1215 x ^{12}}{x ^{12}} + \frac{540 x ^{9}}{x ^{12}} + \frac{135 x ^{6}}{x ^{12}} + \frac{18 x ^{3}}{x ^{12}} + \frac{1}{x ^{12}}

\frac{729 x ^{18}}{x ^{12}} = 729 x^{6}

\frac{1458 x ^{15}}{x ^{12}} = 1458 x^{3}

\frac{1215 x ^{12}}{x ^{12}} = 1215

\frac{540 x ^{9}}{x ^{12}} = \frac{540}{x ^{3}}

\frac{135 x ^{6}}{x ^{12}} = \frac{135}{x ^{6}}

\frac{18 x ^{3}}{x ^{12}} = \frac{18}{x ^{9}}

= 729 x^{6} + 1458 x^{3} + 1215 + \frac{540}{x ^{3}} + \frac{135}{x ^{6}} + \frac{18}{x ^{9}} + \frac{1}{x ^{12}}

s im pl i f y 3 (5 + 1)

e x p an d cos ((t^{2}) (s - 2 t)) (2 s)

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

e x p an d \frac{1}{s ( s - a )}

e x p an d \frac{4 ( - 1 ) ^{n + 1} n - 8 n + ( - 1 ) ^{n} - 1}{4}