faktorisieren 8x^{18}-729y^3z^{15}

Lösung

faktorisieren

8 x^{18} - 729 y^{3} z^{15}

(2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})

Schritte zur Lösung

8 x^{18} - 729 y^{3} z^{15}

Schreibe

8 x^{18}

um:

(2 x^{6})^{3}

Schreibe

729 y^{3} z^{15}

um:

(3^{2} y z^{5})^{3}

= (2 x^{6})^{3} - (3^{2} y z^{5})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(2 x^{6})^{3} - (3^{2} y z^{5})^{3} = (2 x^{6} - 3^{2} y z^{5}) ((2 x^{6})^{2} + 2 x^{6} 3^{2} y z^{5} + (3^{2} y z^{5})^{2})

= (2 x^{6} - 3^{2} y z^{5}) ((2 x^{6})^{2} + 2 x^{6} 3^{2} y z^{5} + (3^{2} y z^{5})^{2})

Vereinfache

(2 x^{6} - 3^{2} y z^{5}) ((2 x^{6})^{2} + 2 x^{6} \cdot 3^{2} y z^{5} + (3^{2} y z^{5})^{2}) : (2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})

= (2 x^{6} - 9 y z^{5}) (4 x^{12} + 18 x^{6} y z^{5} + 81 y^{2} z^{10})

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

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

f a c t or x + Δ x

f a c t or 200

f a c t or x ln (x) - x ln (y)