erweitern ((3x^3-4)^5)/3

Lösung

erweitern

\frac{( 3 x ^{3} - 4 ) ^{5}}{3}

81 x^{15} - 540 x^{12} + 1440 x^{9} - 1920 x^{6} + 1280 x^{3} - \frac{1024}{3}

Schritte zur Lösung

\frac{( 3 x ^{3} - 4 ) ^{5}}{3}

(3 x^{3} - 4)^{5} = 243 x^{15} - 1620 x^{12} + 4320 x^{9} - 5760 x^{6} + 3840 x^{3} - 1024

= \frac{243 x ^{15} - 1620 x ^{12} + 4320 x ^{9} - 5760 x ^{6} + 3840 x ^{3} - 1024}{3}

Wende Bruchregel an:

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

\frac{243 x ^{15} - 1620 x ^{12} + 4320 x ^{9} - 5760 x ^{6} + 3840 x ^{3} - 1024}{3} = \frac{243 x ^{15}}{3} - \frac{1620 x ^{12}}{3} + \frac{4320 x ^{9}}{3} - \frac{5760 x ^{6}}{3} + \frac{3840 x ^{3}}{3} - \frac{1024}{3}

= \frac{243 x ^{15}}{3} - \frac{1620 x ^{12}}{3} + \frac{4320 x ^{9}}{3} - \frac{5760 x ^{6}}{3} + \frac{3840 x ^{3}}{3} - \frac{1024}{3}

\frac{243 x ^{15}}{3} = 81 x^{15}

\frac{1620 x ^{12}}{3} = 540 x^{12}

\frac{4320 x ^{9}}{3} = 1440 x^{9}

\frac{5760 x ^{6}}{3} = 1920 x^{6}

\frac{3840 x ^{3}}{3} = 1280 x^{3}

= 81 x^{15} - 540 x^{12} + 1440 x^{9} - 1920 x^{6} + 1280 x^{3} - \frac{1024}{3}

e x p an d \frac{s}{( s ^{2} + 10 s + 29 ) ^{2}}

e x p an d a \cdot f [b (x + c)] + d

e x p an d, (2^{2 x} - 3) (2^{x} + 4)

e x p an d \frac{( e ^{- 3 s} )}{( s + 1 ) ( 5 s + 1 )}

e x p an d 1 + C (i - 1, j - 1)