erweitern ((2x^3+3)^6)/(x^{12)}

Lösung

erweitern

\frac{( 2 x ^{3} + 3 ) ^{6}}{x ^{12}}

64 x^{6} + 576 x^{3} + 2160 + \frac{4320}{x ^{3}} + \frac{4860}{x ^{6}} + \frac{2916}{x ^{9}} + \frac{729}{x ^{12}}

Schritte zur Lösung

\frac{( 2 x ^{3} + 3 ) ^{6}}{x ^{12}}

(2 x^{3} + 3)^{6} = 64 x^{18} + 576 x^{15} + 2160 x^{12} + 4320 x^{9} + 4860 x^{6} + 2916 x^{3} + 729

= \frac{64 x ^{18} + 576 x ^{15} + 2160 x ^{12} + 4320 x ^{9} + 4860 x ^{6} + 2916 x ^{3} + 729}{x ^{12}}

Wende Bruchregel an:

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

\frac{64 x ^{18} + 576 x ^{15} + 2160 x ^{12} + 4320 x ^{9} + 4860 x ^{6} + 2916 x ^{3} + 729}{x ^{12}} = \frac{64 x ^{18}}{x ^{12}} + \frac{576 x ^{15}}{x ^{12}} + \frac{2160 x ^{12}}{x ^{12}} + \frac{4320 x ^{9}}{x ^{12}} + \frac{4860 x ^{6}}{x ^{12}} + \frac{2916 x ^{3}}{x ^{12}} + \frac{729}{x ^{12}}

= \frac{64 x ^{18}}{x ^{12}} + \frac{576 x ^{15}}{x ^{12}} + \frac{2160 x ^{12}}{x ^{12}} + \frac{4320 x ^{9}}{x ^{12}} + \frac{4860 x ^{6}}{x ^{12}} + \frac{2916 x ^{3}}{x ^{12}} + \frac{729}{x ^{12}}

\frac{64 x ^{18}}{x ^{12}} = 64 x^{6}

\frac{576 x ^{15}}{x ^{12}} = 576 x^{3}

\frac{2160 x ^{12}}{x ^{12}} = 2160

\frac{4320 x ^{9}}{x ^{12}} = \frac{4320}{x ^{3}}

\frac{4860 x ^{6}}{x ^{12}} = \frac{4860}{x ^{6}}

\frac{2916 x ^{3}}{x ^{12}} = \frac{2916}{x ^{9}}

= 64 x^{6} + 576 x^{3} + 2160 + \frac{4320}{x ^{3}} + \frac{4860}{x ^{6}} + \frac{2916}{x ^{9}} + \frac{729}{x ^{12}}

e x p an d (A + Bt) e^{s t}

e x p an d (12 - - 12 - i) 28

e x p an d L in (2 x + 1) + ln (x + 2)

e x p an d 5 (\frac{227 - 5 y}{6} + 4 y = 188)

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