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Beliebt Algebra >

faktorisieren x^{16}-y^{16}

Lösung

faktorisieren

x^{16} - y^{16}

Lösung

(x^{8} + y^{8}) (x^{4} + y^{4}) (x^{2} + y^{2}) (x + y) (x - y)

Schritte zur Lösung

x^{16} - y^{16}

x^{16} = (x^{8})^{2}

y^{16} = (y^{8})^{2}

= (x^{8})^{2} - (y^{8})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{8})^{2} - (y^{8})^{2} = (x^{8} + y^{8}) (x^{8} - y^{8})

= (x^{8} + y^{8}) (x^{8} - y^{8})

Faktorisiere

x^{8} - y^{8} : (x^{4} + y^{4}) (x^{2} + y^{2}) (x + y) (x - y)

= (x^{8} + y^{8}) (x^{4} + y^{4}) (x^{2} + y^{2}) (x + y) (x - y)

Beliebte Beispiele

\frac{x}{2} + 11 = - 1

3 x - 1 = 10

vereinfachen (t^2th-2h^2)/(3t-6h)

s im pl i f y \frac{t ^{2} t h - 2 h ^{2}}{3 t - 6 h}

faktorisieren x^2-(x+2y)^2

f a c t or x^{2} - (x + 2 y)^{2}

x^{2} + 2 x - 3 \leq 0