faktorisieren 27x^6+y^3

Lösung

faktorisieren

27 x^{6} + y^{3}

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

Schritte zur Lösung

27 x^{6} + y^{3}

Wende Exponentenregel an

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

Wende Formel zur Summe von dritten Potenzen an:

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

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

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

Vereinfache

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

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

f a c t or 18 x^{8} - 9 x^{7} y^{4} + 27 y^{9}

s im pl i f y 20 a^{2} b^{4}

e x p an d - 2 x y (9 x^{2} - 6 x y + 27 x^{2} y)

s im pl i f y (x - 2)^{2} - 5 (x - 2)

s im pl i f y ∣ 9 - 3 π ∣ + 9