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Beliebt Algebra >

faktorisieren a^3b^6+8c^3

Lösung

faktorisieren

a^{3} b^{6} + 8 c^{3}

Lösung

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

Schritte zur Lösung

a^{3} b^{6} + 8 c^{3}

Schreibe

a^{3} b^{6}

um:

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

Schreibe

8 c^{3}

um:

(2 c)^{3}

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

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

Vereinfache

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

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

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