faktorisieren sin^{22}(a)+cos^{22}(a)

Lösung

faktorisieren

sin^{22} (a) + cos^{22} (a)

(sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - sin^{18} (a) cos^{2} (a) + sin^{16} (a) cos^{4} (a) - sin^{14} (a) cos^{6} (a) + sin^{12} (a) cos^{8} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

Schritte zur Lösung

sin^{22} (a) + cos^{22} (a)

Schreibe

sin^{22} (a) + cos^{22} (a)

um:

(sin^{2} (a))^{11} + (cos^{2} (a))^{11}

= (sin^{2} (a))^{11} + (cos^{2} (a))^{11}

Wende Regel zum Faktorisieren an:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

(sin^{2} (a))^{11} + (cos^{2} (a))^{11} = (sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - cos^{2} (a) sin^{18} (a) + cos^{4} (a) sin^{16} (a) - cos^{6} (a) sin^{14} (a) + cos^{8} (a) sin^{12} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

= (sin^{2} (a) + cos^{2} (a)) (sin^{20} (a) - cos^{2} (a) sin^{18} (a) + cos^{4} (a) sin^{16} (a) - cos^{6} (a) sin^{14} (a) + cos^{8} (a) sin^{12} (a) - cos^{10} (a) sin^{10} (a) + cos^{12} (a) sin^{8} (a) - cos^{14} (a) sin^{6} (a) + cos^{16} (a) sin^{4} (a) - cos^{18} (a) sin^{2} (a) + cos^{20} (a))

f a c t or (4 x^{10}) - (4 x^{5}) + 1

f a c t or 8^{3} + 2 7^{3}

s im pl i f y \cdot + 5

f a c t or 4 x^{2} + 7 - 3

f a c t or 2 x - 3 y + (- 5)