faktorisieren x^3y^3-z^3

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Schreibe

x^{3} y^{3}

um:

(x y)^{3}

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

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

Vereinfache

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

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

f a c t or e^{j t} + e^{- j t}

f a c t or (x + 3) 2 + 14 (x + 3) + 49

f a c t or 3 - 2 + 23 i

f a c t or 8 cosh (ln (x)) + 4 sinh (ln (x))

f a c t or [(4 y^{2} - 3) + z]^{2}