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

Lösung

faktorisieren

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

7 (4 x - 5) (x^{2} - x + 1)

Schritte zur Lösung

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

Wende Formel zur Summe von dritten Potenzen an:

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

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

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

Fasse zusammen

= (4 x - 5) ((3 x - 2)^{2} - (x - 3) (3 x - 2) + (x - 3)^{2})

Faktorisiere

(3 x - 2)^{2} - (x - 3) (3 x - 2) + (x - 3)^{2} : 7 (x^{2} - x + 1)

= 7 (4 x - 5) (x^{2} - x + 1)

f a c t or [(a + 3 b) + 4 c] [(a + 3 b) + 9 c]

f a c t or z^{6} + 6 z^{4} + 12 z^{2} + 8

f a c t or l {e^{2 t} cosh (t)}

f (x) = 25 (sec (5 x))^{2}

f a c t or (a + b)^{2} - (a - b^{2})