faktorisieren (m-2)^3+(m-3)^3

Lösung

faktorisieren

(m - 2)^{3} + (m - 3)^{3}

(2 m - 5) (m^{2} - 5 m + 7)

Schritte zur Lösung

(m - 2)^{3} + (m - 3)^{3}

Wende Formel zur Summe von dritten Potenzen an:

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

(m - 2)^{3} + (m - 3)^{3} = ((m - 2) + (m - 3)) ((m - 2)^{2} - (m - 3) (m - 2) + (m - 3)^{2})

= ((m - 3) + (m - 2)) ((m - 3)^{2} - (m - 3) (m - 2) + (m - 2)^{2})

Fasse zusammen

= (2 m - 5) ((m - 2)^{2} - (m - 3) (m - 2) + (m - 3)^{2})

Multipliziere aus

(m - 2)^{2} - (m - 3) (m - 2) + (m - 3)^{2} : m^{2} - 5 m + 7

= (2 m - 5) (m^{2} - 5 m + 7)

f a c t or e^{3} - e^{2}

f a c t or 15 a t + 3 b t + 5 a s + b s

f a c t or \cdot (- 5)

f a c t or + (- 4)

f a c t or 3 a c + 2 b c - 6 a d - 4 b d