Wie bewerten Sie # 3x ^ 2 - 27 (2-x) ^ 2 #?

Antworten:

# = - 12 (x-3) (2x-3) #

Erläuterung:

# 3x ^ 2-27 (2-x) ^ 2 #
# = 3x ^ 2-27 (4 + x ^ 2-4x) #
# = 3x ^ 2-27 (4) -27x ^ 2 + 27 (4x) #
# = 3x ^ 2-108-27x ^ 2 + 108x #
# = - 24x ^ 2 + 108x-108 #
# = - 12 (2x ^ 2-9x + 9) #
# = - 12 (2x ^ 2-6x-3x + 9) #
# = - 12 (2x (x-3) -3 (x-3)) #
# = - 12 (x-3) (2x-3) #