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

Lösung

erweitern

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

1 - \frac{3}{x ^{2}} + \frac{3}{x ^{4}} - \frac{1}{x ^{6}}

Schritte zur Lösung

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

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

(x^{2})^{3} : x^{6}

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

(x^{2} - 1)^{3} = x^{6} - 3 x^{4} + 3 x^{2} - 1

= \frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{x ^{6}}

Wende Bruchregel an:

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

\frac{x ^{6} - 3 x ^{4} + 3 x ^{2} - 1}{x ^{6}} = \frac{x ^{6}}{x ^{6}} - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

= \frac{x ^{6}}{x ^{6}} - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Wende Regel an

\frac{a}{a} = 1

\frac{x ^{6}}{x ^{6}} = 1

= 1 - \frac{3 x ^{4}}{x ^{6}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Streiche

\frac{3 x ^{4}}{x ^{6}} : \frac{3}{x ^{2}}

= 1 - \frac{3}{x ^{2}} + \frac{3 x ^{2}}{x ^{6}} - \frac{1}{x ^{6}}

Streiche

\frac{3 x ^{2}}{x ^{6}} : \frac{3}{x ^{4}}

= 1 - \frac{3}{x ^{2}} + \frac{3}{x ^{4}} - \frac{1}{x ^{6}}

e x p an d e^{x} (1 + e^{x})^{10}

e x p an d - 7.5 + 7.5 (p = 50 - 4 p^{5})

e x p an d (- 3 x^{5})^{3}

e x p an d 2 π (x - 1) (8 x - x^{2} - 12)

\frac{\partial}{\partial y} ((x) (x^{2} + y^{2}))