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

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Wende Formel zur Summe von dritten Potenzen an:

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

(sin^{2} (x))^{3} + (cos^{2} (x))^{3} = (sin^{2} (x) + cos^{2} (x)) (sin^{4} (x) - sin^{2} (x) cos^{2} (x) + cos^{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 (x) + (8)

f a c t or (y^{'} (t))^{2} + y^{'} (t)

f a c t or 2 x + 5 x - 12

f a c t or 6 x y - 4 x - 2 z + 3 yz

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