faktorisieren y^6-x^6

Lösung

faktorisieren

y^{6} - x^{6}

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

Schritte zur Lösung

y^{6} - x^{6}

y^{6} = (y^{3})^{2}

x^{6} = (x^{3})^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Faktorisiere

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

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

Faktorisiere

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

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

x^{2} - 4 x + 85 = 0

f a c t or x^{5} - x^{4} y^{3}

1 + \frac{x + 1}{3} = x - \frac{3 x + 1}{8}

f a c t or x^{2} - 27 x y - 90 y^{2}

3 x^{2} - 18 x + 5 = 47