faktorisieren cos^8(x)-2cos^4(x)+1

Lösung

faktorisieren

cos^{8} (x) - 2 cos^{4} (x) + 1

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

Schritte zur Lösung

cos^{8} (x) - 2 cos^{4} (x) + 1

Angenommen

u = cos^{2} (x)

= 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 = cos^{2} (x)

ein

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

Faktorisiere

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

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

Faktorisiere

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

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

Fasse zusammen

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

f (x) = (sin (8 x))^{4}

f a c t or x - (x - y)

f a c t or 4 9^{2} - 16

f a c t or 25 e^{4} - 30 e^{2} f + 9 f^{2}

s im pl i f y [- 22.22]