2. Упростите выражение: a) (c-2)(c+3)-(c-1)²; 6) 3(a+c)²-6ac.

Решение:

1. \( (c-2)(c+3)-(c-1)^2 = (c^2 + 3c - 2c - 6) - (c^2 - 2c + 1) = (c^2 + c - 6) - c^2 + 2c - 1 = c^2 + c - 6 - c^2 + 2c - 1 = 3c - 7 \)
2. \( 3(a+c)^2 - 6ac = 3(a^2 + 2ac + c^2) - 6ac = 3a^2 + 6ac + 3c^2 - 6ac = 3a^2 + 3c^2 \)

Ответ: 1) \( 3c - 7 \); 2) \( 3a^2 + 3c^2 \).