faktorisieren (a+b)^3-(b-c)^3

Lösung

faktorisieren

(a + b)^{3} - (b - c)^{3}

(a + c) (3 b^{2} + 3 ab - 3 b c + a^{2} + c^{2} - a c)

Schritte zur Lösung

(a + b)^{3} - (b - c)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(a + b)^{3} - (b - c)^{3} = ((a + b) - (b - c)) ((a + b)^{2} + (b - c) (a + b) + (b - c)^{2})

= ((a + b) - (b - c)) ((b - c)^{2} + (b - c) (a + b) + (a + b)^{2})

Fasse zusammen

= (a + c) ((a + b)^{2} + (b - c) (a + b) + (b - c)^{2})

Multipliziere aus

(a + b)^{2} + (b - c) (a + b) + (b - c)^{2} : 3 b^{2} + 3 ab - 3 b c + a^{2} + c^{2} - a c

= (a + c) (a^{2} + 3 ab - a c + 3 b^{2} + c^{2} - 3 b c)

f a c t or 2 (x + 1) - 4 (x + 1)

f a c t or 1 6^{4} - 81

f a c t or 2 x^{2} - a x^{2} - 2 y + a y

f a c t or 8 e^{3} f^{6} - 125 g^{3}

f (x) = (cos (11 x))^{2}