Вариант 2. Вынесите общий множитель за скобки: 1) a (x - y) + b (x - y) 2) x (a + 5) - (a + 5) 3) 3 (b-2) -a (2-b) 4) (a - b)² + 4b (a – b) 5) 6 (x - y)² + y (y−x) 6) 5 (a - b) – (a – b)²

Решение:

1. \( a (x - y) + b (x - y) = \mathbf{(x - y)(a + b)} \)
2. \( x (a + 5) - (a + 5) = x (a + 5) - 1 (a + 5) = \mathbf{(a + 5)(x - 1)} \)
3. \( 3 (b - 2) - a (2 - b) = 3 (b - 2) + a (b - 2) = \mathbf{(b - 2)(3 + a)} \)
4. \( (a - b)^2 + 4b (a - b) = (a - b) [(a - b) + 4b] = (a - b) (a + 3b) = \mathbf{(a - b)(a + 3b)} \)
5. \( 6 (x - y)^2 + y (y - x) = 6 (x - y)^2 - y (x - y) = (x - y) [6 (x - y) - y] = (x - y) (6x - 6y - y) = \mathbf{(x - y)(6x - 7y)} \)
6. \( 5 (a - b) - (a - b)^2 = (a - b) [5 - (a - b)] = (a - b) (5 - a + b) = \mathbf{(a - b)(5 - a + b)} \)

Ответ: 1) \( (x - y)(a + b) \); 2) \( (a + 5)(x - 1) \); 3) \( (b - 2)(3 + a) \); 4) \( (a - b)(a + 3b) \); 5) \( (x - y)(6x - 7y) \); 6) \( (a - b)(5 - a + b) \).