erweitern ((2x^3+1)^6)/(x^{12)}

Lösung

erweitern

\frac{( 2 x ^{3} + 1 ) ^{6}}{x ^{12}}

64 x^{6} + 192 x^{3} + 240 + \frac{160}{x ^{3}} + \frac{60}{x ^{6}} + \frac{12}{x ^{9}} + \frac{1}{x ^{12}}

Schritte zur Lösung

\frac{( 2 x ^{3} + 1 ) ^{6}}{x ^{12}}

(2 x^{3} + 1)^{6} = 64 x^{18} + 192 x^{15} + 240 x^{12} + 160 x^{9} + 60 x^{6} + 12 x^{3} + 1

= \frac{64 x ^{18} + 192 x ^{15} + 240 x ^{12} + 160 x ^{9} + 60 x ^{6} + 12 x ^{3} + 1}{x ^{12}}

Wende Bruchregel an:

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

\frac{64 x ^{18} + 192 x ^{15} + 240 x ^{12} + 160 x ^{9} + 60 x ^{6} + 12 x ^{3} + 1}{x ^{12}} = \frac{64 x ^{18}}{x ^{12}} + \frac{192 x ^{15}}{x ^{12}} + \frac{240 x ^{12}}{x ^{12}} + \frac{160 x ^{9}}{x ^{12}} + \frac{60 x ^{6}}{x ^{12}} + \frac{12 x ^{3}}{x ^{12}} + \frac{1}{x ^{12}}

= \frac{64 x ^{18}}{x ^{12}} + \frac{192 x ^{15}}{x ^{12}} + \frac{240 x ^{12}}{x ^{12}} + \frac{160 x ^{9}}{x ^{12}} + \frac{60 x ^{6}}{x ^{12}} + \frac{12 x ^{3}}{x ^{12}} + \frac{1}{x ^{12}}

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

\frac{192 x ^{15}}{x ^{12}} = 192 x^{3}

\frac{240 x ^{12}}{x ^{12}} = 240

\frac{160 x ^{9}}{x ^{12}} = \frac{160}{x ^{3}}

\frac{60 x ^{6}}{x ^{12}} = \frac{60}{x ^{6}}

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

= 64 x^{6} + 192 x^{3} + 240 + \frac{160}{x ^{3}} + \frac{60}{x ^{6}} + \frac{12}{x ^{9}} + \frac{1}{x ^{12}}

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

e x p an d 1 4^{4 x - x^{2}} e^{3 x^{2}} (2 - x ln (7) + 3 x)

e x p an d \frac{1}{4} (8 x + 4 = 2 x - 4)

e x p an d (3, - 2) y (1, - 4)

e x p an d \frac{( k \cdot e ^{- o x} )}{( t x + 1 ) x}