erweitern ((-5x^8+1)^4)/(x^{28)}

Lösung

erweitern

\frac{( - 5 x ^{8} + 1 ) ^{4}}{x ^{28}}

625 x^{4} - \frac{500}{x ^{4}} + \frac{150}{x ^{12}} - \frac{20}{x ^{20}} + \frac{1}{x ^{28}}

Schritte zur Lösung

\frac{( - 5 x ^{8} + 1 ) ^{4}}{x ^{28}}

(- 5 x^{8} + 1)^{4} = 625 x^{32} - 500 x^{24} + 150 x^{16} - 20 x^{8} + 1

= \frac{625 x ^{32} - 500 x ^{24} + 150 x ^{16} - 20 x ^{8} + 1}{x ^{28}}

Wende Bruchregel an:

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

\frac{625 x ^{32} - 500 x ^{24} + 150 x ^{16} - 20 x ^{8} + 1}{x ^{28}} = \frac{625 x ^{32}}{x ^{28}} - \frac{500 x ^{24}}{x ^{28}} + \frac{150 x ^{16}}{x ^{28}} - \frac{20 x ^{8}}{x ^{28}} + \frac{1}{x ^{28}}

= \frac{625 x ^{32}}{x ^{28}} - \frac{500 x ^{24}}{x ^{28}} + \frac{150 x ^{16}}{x ^{28}} - \frac{20 x ^{8}}{x ^{28}} + \frac{1}{x ^{28}}

\frac{625 x ^{32}}{x ^{28}} = 625 x^{4}

\frac{500 x ^{24}}{x ^{28}} = \frac{500}{x ^{4}}

\frac{150 x ^{16}}{x ^{28}} = \frac{150}{x ^{12}}

\frac{20 x ^{8}}{x ^{28}} = \frac{20}{x ^{20}}

= 625 x^{4} - \frac{500}{x ^{4}} + \frac{150}{x ^{12}} - \frac{20}{x ^{20}} + \frac{1}{x ^{28}}

e x p an d ((A + A^{^{'}}) + B) D

e x p an d - 0.25 (1 - x) ln (1 - x)

e x p an d \frac{3}{4} (x + 2 = - 1)

e x p an d \frac{1 - x ^{2}}{x ^{3} ( x ^{2} + 5 )}

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