faktorisieren w^3-8t^3n^6

Lösung

faktorisieren

w^{3} - 8 t^{3} n^{6}

(w - 2 n^{2} t) (w^{2} + 2 n^{2} wt + 4 n^{4} t^{2})

Schritte zur Lösung

w^{3} - 8 t^{3} n^{6}

Schreibe

8 t^{3} n^{6}

um:

(2 t n^{2})^{3}

= w^{3} - (2 t n^{2})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

w^{3} - (2 t n^{2})^{3} = (w - 2 t n^{2}) (w^{2} + w 2 t n^{2} + (2 t n^{2})^{2})

= (w - 2 t n^{2}) (w^{2} + w 2 t n^{2} + (2 t n^{2})^{2})

Vereinfache

(w - 2 t n^{2}) (w^{2} + w \cdot 2 t n^{2} + (2 t n^{2})^{2}) : (w - 2 n^{2} t) (w^{2} + 2 n^{2} wt + 4 n^{4} t^{2})

= (w - 2 n^{2} t) (w^{2} + 2 n^{2} wt + 4 n^{4} t^{2})

f a c t or + 10 m + 3 (n - 8) - 7 (m - 12) + 9 n

f a c t or \frac{d ^{2} - 3 d - 18}{d + 3}

f (c) = c - 9

f a c t or e^{6 x} - e^{x}

f a c t or \frac{3}{4 \frac{5}{6}}