faktorisieren cos^6(x)+sin^6(x)

Lösung

faktorisieren

cos^{6} (x) + sin^{6} (x)

(cos^{2} (x) + sin^{2} (x)) (cos^{4} (x) - sin^{2} (x) cos^{2} (x) + sin^{4} (x))

Schritte zur Lösung

cos^{6} (x) + sin^{6} (x)

Schreibe

cos^{6} (x) + sin^{6} (x)

um:

(cos^{2} (x))^{3} + (sin^{2} (x))^{3}

= (cos^{2} (x))^{3} + (sin^{2} (x))^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

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

= (sin^{2} (x) + cos^{2} (x)) (sin^{4} (x) - sin^{2} (x) cos^{2} (x) + cos^{4} (x))

f a c t or a c + b c + a d + b d

f a c t or 2 j^{17} + 32 j^{482}

f a c t or 16 r^{2} - π r^{2}

f a c t or 2 b^{3} + 3 c^{3} - 2 b^{3} x - 3 c^{3} x

f a c t or cos (x^{2} - 1)