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

Lösung

erweitern

(3 a + 3 b)^{3}

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

Schritte zur Lösung

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

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

Vereinfache

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

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

e x p an d x^{5} (e x^{3} - sin (x^{2}))

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

e x p an d \frac{1}{( j w ) ( a + j w )}

e x p an d \frac{d}{d x} (1 - x) + c \cdot x (x - 1)

s im pl i f y (\frac{3 m}{4} - \frac{1}{6}) (\frac{m}{4} - \frac{5}{6})