faktorisieren (p+q)^3-(p-q)^3

Lösung

faktorisieren

(p + q)^{3} - (p - q)^{3}

2 q (3 p^{2} + q^{2})

Schritte zur Lösung

(p + q)^{3} - (p - q)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(p + q)^{3} - (p - q)^{3} = ((p + q) - (p - q)) ((p + q)^{2} + (p - q) (p + q) + (p - q)^{2})

= ((p + q) - (p - q)) ((p - q)^{2} + (p - q) (p + q) + (p + q)^{2})

Fasse zusammen

= 2 q ((p + q)^{2} + (p - q) (p + q) + (p - q)^{2})

Multipliziere aus

(p + q)^{2} + (p - q) (p + q) + (p - q)^{2} : 3 p^{2} + q^{2}

= 2 q (3 p^{2} + q^{2})

f a c t or 147

f a c t or 6 x^{2} + 3 x^{7}

f a c t or x^{6} - 27 x^{4} + 243 x^{2} - 729

f a c t or 3 (r - 2)^{2} - 7 (r - 2) + 2

f a c t or 10 x - 10 y - x^{5} + x^{4} y