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Beliebt Algebra >

faktorisieren x^8-4x^6+6x^4-4x^2+1

Lösung

faktorisieren

x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1

Lösung

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

Schritte zur Lösung

x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1

Angenommen

u = x^{2}

= u^{4} - 4 u^{3} + 6 u^{2} - 4 u + 1

Faktorisiere

u^{4} - 4 u^{3} + 6 u^{2} - 4 u + 1 : (u - 1) (u - 1) (u - 1) (u - 1)

= (u - 1) (u - 1) (u - 1) (u - 1)

Setze in

u = x^{2}

ein

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

Faktorisiere

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

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

Faktorisiere

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

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

Faktorisiere

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

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

Faktorisiere

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

= (x + 1) (x - 1) (x + 1) (x - 1) (x + 1) (x - 1) (x + 1) (x - 1)

Fasse zusammen

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

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