faktorisieren m^{18}y^3-n^3z^{18}

Lösung

faktorisieren

m^{18} y^{3} - n^{3} z^{18}

(m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

Schritte zur Lösung

m^{18} y^{3} - n^{3} z^{18}

Schreibe

m^{18} y^{3}

um:

(m^{6} y)^{3}

Schreibe

n^{3} z^{18}

um:

(n z^{6})^{3}

= (m^{6} y)^{3} - (n z^{6})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(m^{6} y)^{3} - (n z^{6})^{3} = (m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2})

= (m^{6} y - n z^{6}) ((n z^{6})^{2} + n z^{6} m^{6} y + (m^{6} y)^{2})

Vereinfache

(m^{6} y - n z^{6}) ((m^{6} y)^{2} + n z^{6} m^{6} y + (n z^{6})^{2}) : (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

= (m^{6} y - n z^{6}) (m^{12} y^{2} + n m^{6} y z^{6} + n^{2} z^{12})

f a c t or (x + 2 y)^{3} + 1

f a c t or x^{3} - 6 x - 5 x + 30

f a c t or x (2 y)

f (x) = (sin (2 x))^{4}

f a c t or cos (f (t))