faktorisieren x^4-7x^2y^2+y^4

Lösung

faktorisieren

x^{4} - 7 x^{2} y^{2} + y^{4}

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

Schritte zur Lösung

x^{4} - 7 x^{2} y^{2} + y^{4}

Addiere und subtrahiere

9 x^{2} y^{2}

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

Faktorisiere

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

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

Wende Exponentenregel an

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

Faktorisiere

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

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

e x p an d (2 x^{2} + 3 x - 7) (3 x^{2} - 5 x + 4)

s im pl i f y \frac{3}{p - 2 p}

s im pl i f y (x^{11} sin (x^{4}))^{22}

s im pl i f y (x^{\frac{- 2}{3}} \cdot y^{\frac{- 3}{4}})^{- 6}

s im pl i f y 2 x - 2 x + y