faktorisieren x^8-81y^8

Lösung

faktorisieren

x^{8} - 81 y^{8}

(x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

Schritte zur Lösung

x^{8} - 81 y^{8}

x^{8} = (x^{4})^{2}

81 y^{8} = (9 y^{4})^{2}

= (x^{4})^{2} - (9 y^{4})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{4})^{2} - (9 y^{4})^{2} = (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

= (x^{4} + 9 y^{4}) (x^{4} - 9 y^{4})

Faktorisiere

x^{4} - 9 y^{4} : (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

= (x^{4} + 9 y^{4}) (x^{2} + 3 y^{2}) (x^{2} - 3 y^{2})

s im pl i f y (\frac{1}{2} - \frac{1}{2} i)^{- 7}

- 5 \frac{3}{4} - 3 \frac{1}{2}

s im pl i f y (sin (t) - cos (t))^{2}

s im pl i f y \frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

s im pl i f y - \frac{1}{2} i^{3} (- 9 - 4) - 3 i^{2}