erweitern (p^{2/3}-q^{1/3})^3

Lösung

erweitern

(p^{\frac{2}{3}} - q^{\frac{1}{3}})^{3}

p^{2} - 3 p^{\frac{4}{3}} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} q^{\frac{2}{3}} - q

Schritte zur Lösung

(p^{\frac{2}{3}} - q^{\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}

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

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

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

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

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

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

= p^{2} - 3 p^{\frac{4}{3}} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} q^{\frac{2}{3}} - q

s im pl i f y 10 (4 lo g_{2} (40) + 48 lo g_{2} (1300))

e x p an d \frac{9}{( x + 5 ) ^{2}}

s im pl i f y (P + \frac{a}{V ^{2}}) (V - b) - RT

e x p an d \frac{2 x + 2 h}{x ^{2} + 2 x h + h ^{2} + 1} - \frac{2 x}{x ^{2} + 1}

e x p an d ((3 6^{2} - y^{2}) - 13.5)^{2}