erweitern ((2x^3-1)^6)/(64x^6)

Lösung

erweitern

\frac{( 2 x ^{3} - 1 ) ^{6}}{64 x ^{6}}

x^{12} - 3 x^{9} + \frac{15 x ^{6}}{4} - \frac{5 x ^{3}}{2} + \frac{15}{16} - \frac{3}{16 x ^{3}} + \frac{1}{64 x ^{6}}

Schritte zur Lösung

\frac{( 2 x ^{3} - 1 ) ^{6}}{64 x ^{6}}

(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}{64 x ^{6}}

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

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

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

\frac{192 x ^{15}}{64 x ^{6}} = 3 x^{9}

\frac{240 x ^{12}}{64 x ^{6}} = \frac{15 x ^{6}}{4}

\frac{160 x ^{9}}{64 x ^{6}} = \frac{5 x ^{3}}{2}

\frac{60 x ^{6}}{64 x ^{6}} = \frac{15}{16}

\frac{12 x ^{3}}{64 x ^{6}} = \frac{3}{16 x ^{3}}

= x^{12} - 3 x^{9} + \frac{15 x ^{6}}{4} - \frac{5 x ^{3}}{2} + \frac{15}{16} - \frac{3}{16 x ^{3}} + \frac{1}{64 x ^{6}}

e x p an d y (2 x e^{x y} + e^{x y} y x^{2})

e x p an d ln (x - 3) (x + 3)

e x p an d - \frac{g ( 5 u - 4 )}{9}

e x p an d, 2 (w + 5) - 5 w

e x p an d \frac{16}{( 3 x + 3 ) ( x + 1 )}