erweitern (x^{2/3}-y^{1/3})^3

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

(x^{\frac{2}{3}})^{2} = x^{\frac{4}{3}}

(y^{\frac{1}{3}})^{2} = y^{\frac{2}{3}}

(y^{\frac{1}{3}})^{3} = y

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

s im pl i f y (x + 37) (x - 7)

s im pl i f y \frac{1}{( 1 - i 3 ) ^{4}}

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

e x p an d (x^{2} - x + \frac{1}{6})^{2}

e x p an d (\frac{x ^{2}}{2} + \frac{4}{x})^{6}