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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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

3 x^{\frac{1}{3}} \cdot 1^{2} = 3 x^{\frac{1}{3}}

1^{3} = 1

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

e x p an d (\frac{5}{1 - x} - \frac{4}{1 + 2 x})^{4}

e x p an d (1 + 3) x

s im pl i f y 23 (2 x + 33)

e x p an d \frac{5}{( 3 3 x + 4 + 1 ) ^{4}}

e x p an d \frac{( - m ^{2} + a ^{2} ) ( a ^{2} + am + m ^{2} )}{4 + m}