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Beliebt Algebra >

faktorisieren w^3y^{12}+1728x^6

Lösung

faktorisieren

w^{3} y^{12} + 1728 x^{6}

Lösung

(w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

Schritte zur Lösung

w^{3} y^{12} + 1728 x^{6}

Schreibe

w^{3} y^{12}

um:

(w y^{4})^{3}

Schreibe

1728 x^{6}

um:

(12 x^{2})^{3}

= (w y^{4})^{3} + (12 x^{2})^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(w y^{4})^{3} + (12 x^{2})^{3} = (w y^{4} + 12 x^{2}) ((w y^{4})^{2} - 12 x^{2} w y^{4} + (12 x^{2})^{2})

= (12 x^{2} + w y^{4}) ((12 x^{2})^{2} - 12 x^{2} w y^{4} + (w y^{4})^{2})

Vereinfache

(w y^{4} + 12 x^{2}) ((w y^{4})^{2} - 12 x^{2} w y^{4} + (12 x^{2})^{2}) : (w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

= (w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

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