faktorisieren x^6+x^3-y^6-y^3

Lösung

faktorisieren

x^{6} + x^{3} - y^{6} - y^{3}

(x - y) (x^{2} + x y + y^{2}) (x^{3} + y^{3} + 1)

Schritte zur Lösung

x^{6} + x^{3} - y^{6} - y^{3}

Faktorisiere

x^{6} - y^{6} : (x + y) (x^{2} - x y + y^{2}) (x - y) (x^{2} + x y + y^{2})

Faktorisiere

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

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

Klammere gleiche Terme aus

(x - y) (x^{2} + x y + y^{2}) : (x - y) (x^{2} + x y + y^{2}) ((x + y) (x^{2} - x y + y^{2}) + 1)

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

Schreibe

(x + y) (x^{2} - x y + y^{2}) + 1

um:

x^{3} + y^{3} + 1

= (x - y) (x^{2} + x y + y^{2}) (x^{3} + y^{3} + 1)

e x p an d (a - 11) (a + 11)

e x p an d (2 x + 3) (x + 9)

s im pl i f y (u^{7})^{- 4}

s im pl i f y - arctan (\frac{- e ^{x}}{4})

e x p an d (7 w + 5) (7 w - 7 u + 3)