faktorisieren x^3y^3-64z^3

Lösung

faktorisieren

x^{3} y^{3} - 64 z^{3}

(x y - 4 z) (x^{2} y^{2} + 4 x yz + 16 z^{2})

Schritte zur Lösung

x^{3} y^{3} - 64 z^{3}

Schreibe

x^{3} y^{3}

um:

(x y)^{3}

Schreibe

64 z^{3}

um:

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

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

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

(x y - 2^{2} z) ((x y)^{2} + 2^{2} z x y + (2^{2} z)^{2}) : (x y - 4 z) (x^{2} y^{2} + 4 x yz + 16 z^{2})

= (x y - 4 z) (x^{2} y^{2} + 4 x yz + 16 z^{2})

s im pl i f y \frac{1}{3} \cdot \frac{2}{9}

\frac{x + 2}{x - 3} > 0

(x + 3) x - 7 (x + 3) = 0

s im pl i f y (\frac{1}{6})^{- 4}

2 x - 7 = 17