faktorisieren x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4

Lösung

faktorisieren

x^{5} + x^{3} y^{2} + x y^{4} + x^{4} + x^{2} y^{2} + y^{4}

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

Schritte zur Lösung

x^{5} + x^{3} y^{2} + x y^{4} + x^{4} + x^{2} y^{2} + y^{4}

= (x^{5} + x^{3} y^{2} + x y^{4}) + (x^{4} + x^{2} y^{2} + y^{4})

Klammere

x

aus

x^{5} + x^{3} y^{2} + x y^{4}

aus

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

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

Klammere gleiche Terme aus

(x^{4} + x^{2} y^{2} + y^{4}) : (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

= (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

Faktorisiere

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

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

s im pl i f y \frac{6 \cdot 3}{6 + 3}

f a c t or 2 (x + 1)^{2} - 6 (x + 1) + 4

- 15 x + 4 = 6

s im pl i f y \frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6} + \frac{6}{7}

s im pl i f y 697