faktorisieren x^3-z^3y^6

Lösung

faktorisieren

x^{3} - z^{3} y^{6}

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

Schritte zur Lösung

x^{3} - z^{3} y^{6}

Schreibe

z^{3} y^{6}

um:

(z y^{2})^{3}

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

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

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

f a c t or H^{3} P O^{4} + M g (O H) 2

f a c t or 3 x + (2)

f a c t or \frac{14 7 - 2}{3}

f a c t or f (5) d x

s im pl i f y [7.8]