faktorisieren 1+x^8-2x^4

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Angenommen

u = x^{2}

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

Faktorisiere

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

Faktorisiere

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

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

Fasse zusammen

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

f a c t or 2 - x - 20

f a c t or b z + cz - ba - c a

f a c t or a [(b - c) + d]

f a c t or x^{2} + x y + z x + yz

f a c t or f (t) tan (1 + e^{2 t})