erweitern (y^2+x^3)^3

Lösung

erweitern

(y^{2} + x^{3})^{3}

y^{6} + 3 y^{4} x^{3} + 3 y^{2} x^{6} + x^{9}

Schritte zur Lösung

(y^{2} + x^{3})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(y^{2} + x^{3})^{3} = (y^{2})^{3} + 3 (y^{2})^{2} x^{3} + 3 y^{2} (x^{3})^{2} + (x^{3})^{3}

= (y^{2})^{3} + 3 (y^{2})^{2} x^{3} + 3 y^{2} (x^{3})^{2} + (x^{3})^{3}

Vereinfache

(y^{2})^{3} + 3 (y^{2})^{2} x^{3} + 3 y^{2} (x^{3})^{2} + (x^{3})^{3} : y^{6} + 3 y^{4} x^{3} + 3 y^{2} x^{6} + x^{9}

= y^{6} + 3 y^{4} x^{3} + 3 y^{2} x^{6} + x^{9}

e x p an d (x^{2} - 7 x)^{3}

s im pl i f y x^{3} - 2 x^{2} + 2 x^{- 1}

s im pl i f y (\frac{a + 1}{a})^{3}

s im pl i f y (5 a + 3 b)^{3} - (5 a - 3 b)^{3}

s im pl i f y (\frac{1}{4} \cdot x + \frac{2}{7} \cdot y)^{3}