X ^ 6 - 3x ^ 4 + 3x ^ 2 -1? Hvordan faktor det let?

Svar:

# = (x - 1) ^ 3 (x + 1) ^ 3 #

Forklaring:

# "Brug" y = x ^ 2 #

# => y ^ 3 - 3 y ^ 2 + 3 y - 1 = 0 #

# "Vi genkender binomialkoefficienterne 1 3 3 1 fra" (1 + x) ^ 3 #

# => (y - 1) ^ 3 = 0 #

x = 1 (x + 1) ^ 3 = (x - 1) ^ 3 (x + 1) ^ 3 #