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Beliebt Algebra >

faktorisieren x^6+64y^6

Lösung

faktorisieren

x^{6} + 64 y^{6}

Lösung

(x^{2} + 4 y^{2}) (x^{4} - 4 x^{2} y^{2} + 16 y^{4})

Schritte zur Lösung

x^{6} + 64 y^{6}

Wende Exponentenregel an

= (x^{2})^{3} + (4 y^{2})^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(x^{2})^{3} + (4 y^{2})^{3} = (x^{2} + 4 y^{2}) ((x^{2})^{2} - x^{2} \cdot 4 y^{2} + (4 y^{2})^{2})

= (x^{2} + 4 y^{2}) ((x^{2})^{2} - x^{2} \cdot 4 y^{2} + (4 y^{2})^{2})

Vereinfache

(x^{2})^{2} - x^{2} \cdot 4 y^{2} + (4 y^{2})^{2} : x^{4} - 4 x^{2} y^{2} + 16 y^{4}

= (x^{2} + 4 y^{2}) (x^{4} - 4 x^{2} y^{2} + 16 y^{4})

Beliebte Beispiele

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