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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

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

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

s im pl i f y - [3 x - 2 y + (x - 2 y) - 2 (x + y) - 3 (2 x + 1)]

\frac{95}{3}

s im pl i f y x^{2} \cdot 6 x

f a c t or 6 x^{2} - 41 x + 30

s im pl i f y 9 ab - 12 a b^{2} - 6 a^{2} b + 4 a b^{2}