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Beliebt Algebra >

faktorisieren a^3b^6+c^6

Lösung

faktorisieren

a^{3} b^{6} + c^{6}

Lösung

(a b^{2} + c^{2}) (a^{2} b^{4} - a b^{2} c^{2} + c^{4})

Schritte zur Lösung

a^{3} b^{6} + c^{6}

Schreibe

a^{3} b^{6}

um:

(a b^{2})^{3}

= (a b^{2})^{3} + c^{6}

Wende Exponentenregel an:

a^{b c} = (a^{b})^{c}

c^{6} = (c^{2})^{3}

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

Wende Formel zur Summe von dritten Potenzen an:

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

(a b^{2})^{3} + (c^{2})^{3} = (a b^{2} + c^{2}) ((a b^{2})^{2} - a b^{2} c^{2} + c^{4})

= (c^{2} + a b^{2}) ((a b^{2})^{2} - c^{2} a b^{2} + c^{4})

Vereinfache

(a b^{2} + c^{2}) ((a b^{2})^{2} - a b^{2} c^{2} + c^{4}) : (a b^{2} + c^{2}) (a^{2} b^{4} - a b^{2} c^{2} + c^{4})

= (a b^{2} + c^{2}) (a^{2} b^{4} - a b^{2} c^{2} + c^{4})

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