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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

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

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

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