erweitern (x-1/x)^3

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Vereinfache

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

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

e x p an d (2 n)!

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

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

e x p an d (3 t - \frac{4}{p})^{5}

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