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

Lösung

faktorisieren

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

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

\frac{d ^{2}}{d x ^{2}} ((y) (3^{x}))

f a c t or 5 x y + yz - 15 x - 3 z

s im pl i f y - 2 k t + s^{{3}}

s im pl i f y (\frac{3}{2})!