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

Lösung

erweitern

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

8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

(2 x^{3})^{3} - 3 (2 x^{3})^{2} \cdot 3 y^{2} + 3 \cdot 2 x^{3} (3 y^{2})^{2} - (3 y^{2})^{3} : 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

= 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

s im pl i f y 300 - 27

f a c t or 9 x^{2} + 5 x - 4

s im pl i f y (4 a)^{3}

s im pl i f y (3 x - \frac{1}{2} y)^{3}

\frac{26}{25}