erweitern ((3x^2-2)^5)/5

Lösung

erweitern

\frac{( 3 x ^{2} - 2 ) ^{5}}{5}

\frac{243 x ^{10}}{5} - 162 x^{8} + 216 x^{6} - 144 x^{4} + 48 x^{2} - \frac{32}{5}

Schritte zur Lösung

\frac{( 3 x ^{2} - 2 ) ^{5}}{5}

(3 x^{2} - 2)^{5} = 243 x^{10} - 810 x^{8} + 1080 x^{6} - 720 x^{4} + 240 x^{2} - 32

= \frac{243 x ^{10} - 810 x ^{8} + 1080 x ^{6} - 720 x ^{4} + 240 x ^{2} - 32}{5}

Wende Bruchregel an:

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

\frac{243 x ^{10} - 810 x ^{8} + 1080 x ^{6} - 720 x ^{4} + 240 x ^{2} - 32}{5} = \frac{243 x ^{10}}{5} - \frac{810 x ^{8}}{5} + \frac{1080 x ^{6}}{5} - \frac{720 x ^{4}}{5} + \frac{240 x ^{2}}{5} - \frac{32}{5}

= \frac{243 x ^{10}}{5} - \frac{810 x ^{8}}{5} + \frac{1080 x ^{6}}{5} - \frac{720 x ^{4}}{5} + \frac{240 x ^{2}}{5} - \frac{32}{5}

\frac{810 x ^{8}}{5} = 162 x^{8}

\frac{1080 x ^{6}}{5} = 216 x^{6}

\frac{720 x ^{4}}{5} = 144 x^{4}

\frac{240 x ^{2}}{5} = 48 x^{2}

= \frac{243 x ^{10}}{5} - 162 x^{8} + 216 x^{6} - 144 x^{4} + 48 x^{2} - \frac{32}{5}

e x p an d \frac{( 10 x - 5 ) 5}{2}

e x p an d 5 - (2 x = (43) - 1)

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

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

e x p an d e^{(- x - a) 2}