erweitern (\sqrt[3]{a}+2\sqrt[3]{b})^3

Lösung

erweitern

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

a + 6 (3 a)^{2} 3 b + 12 3 b^{2} 3 a + 8 b

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

(3 a + 2 3 b)^{3} = (3 a)^{3} + 3 (3 a)^{2} \cdot 2 3 b + 3 3 a (2 3 b)^{2} + (2 3 b)^{3}

= (3 a)^{3} + 3 (3 a)^{2} \cdot 2 3 b + 3 3 a (2 3 b)^{2} + (2 3 b)^{3}

Vereinfache

(3 a)^{3} + 3 (3 a)^{2} \cdot 2 3 b + 3 3 a (2 3 b)^{2} + (2 3 b)^{3} : a + 6 (3 a)^{2} 3 b + 12 b^{\frac{2}{3}} 3 a + 8 b

= a + 6 (3 a)^{2} 3 b + 12 b^{\frac{2}{3}} 3 a + 8 b

b^{\frac{2}{3}} = 3 b^{2}

= a + 6 (3 a)^{2} 3 b + 12 3 b^{2} 3 a + 8 b

s im pl i f y 2 x (x + 1)

e x p an d \frac{( s + 3 )}{( s ^{2} + 6 s + 34 ) ^{2}}

e x p an d (x - 3 i) (x + 3 i) (x - 2)

e x p an d 4 - 2 (x + Δ x) - 4 - 2 x

e x p an d (\frac{p}{2} - q) (q + \frac{p}{2})