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Beliebt Algebra >

faktorisieren cos^5(x)+sin^5(x)

Lösung

faktorisieren

cos^{5} (x) + sin^{5} (x)

Lösung

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

Schritte zur Lösung

cos^{5} (x) + sin^{5} (x)

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

cos^{5} (x) + sin^{5} (x) = (cos (x) + sin (x)) (cos^{4} (x) - sin (x) cos^{3} (x) + sin^{2} (x) cos^{2} (x) - sin^{3} (x) cos (x) + sin^{4} (x))

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

Beliebte Beispiele

faktorisieren 3(2x+1)(x+5)(2x+1)

f a c t or 3 (2 x + 1) (x + 5) (2 x + 1)

faktorisieren 3^2+5x+2

f a c t or 3^{2} + 5 x + 2

faktorisieren 2log_{2left(x^{4right})}(x)

f a c t or 2 lo g_{2 l e f t (x^{4 r i g h t})} (x)

faktorisieren 2x^{-2}-3x^{-3}

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

faktorisieren (d+1)-5(d+1)

f a c t or (d + 1) - 5 (d + 1)