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Beliebt Algebra >

faktorisieren x^6-1

Lösung

faktorisieren

x^{6} - 1

Lösung

(x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)

Schritte zur Lösung

x^{6} - 1

Wende Exponentenregel an

= (x^{2})^{3} - 1^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(x^{2})^{3} - 1^{3} = (x^{2} - 1) (x^{4} + x^{2} + 1)

= (x^{2} - 1) (x^{4} + x^{2} + 1)

Faktorisiere

x^{2} - 1 : (x + 1) (x - 1)

= (x + 1) (x - 1) (x^{4} + x^{2} + 1)

Faktorisiere

x^{4} + x^{2} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x)

= (x + 1) (x - 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

= (x + 1) (x - 1) (x^{2} + x + 1) (x^{2} - x + 1)

Beliebte Beispiele

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2x+(x-3)/2 =(x-3)/4

2 x + \frac{x - 3}{2} = \frac{x - 3}{4}