128. Упростите выражение: 1) (x - 3)² - 8; 2) 12x - (x + 6)²; 3) (2a - 3b)² - 4a(a – 6b); 4) (2x – 3y)² + (4x + 2y)²; 5) (x - 5)² - x(x + 3); 6) (6a - b)² - (9a – b)(4a + 2b); 7) 3x(5 + x)² – x(3x – 6)²;

Решение:

1. \( (x - 3)^2 - 8 = (x^2 - 6x + 9) - 8 = x^2 - 6x + 1 \)
2. \( 12x - (x + 6)^2 = 12x - (x^2 + 12x + 36) = 12x - x^2 - 12x - 36 = -x^2 - 36 \)
3. \( (2a - 3b)^2 - 4a(a - 6b) = (4a^2 - 12ab + 9b^2) - (4a^2 - 24ab) = 4a^2 - 12ab + 9b^2 - 4a^2 + 24ab = 12ab + 9b^2 \)
4. \( (2x - 3y)^2 + (4x + 2y)^2 = (4x^2 - 12xy + 9y^2) + (16x^2 + 16xy + 4y^2) = 4x^2 - 12xy + 9y^2 + 16x^2 + 16xy + 4y^2 = 20x^2 + 4xy + 13y^2 \)
5. \( (x - 5)^2 - x(x + 3) = (x^2 - 10x + 25) - (x^2 + 3x) = x^2 - 10x + 25 - x^2 - 3x = -13x + 25 \)
6. \( (6a - b)^2 - (9a - b)(4a + 2b) = (36a^2 - 12ab + b^2) - (36a^2 + 18ab - 4ab - 2b^2) = (36a^2 - 12ab + b^2) - (36a^2 + 14ab - 2b^2) = 36a^2 - 12ab + b^2 - 36a^2 - 14ab + 2b^2 = -26ab + 3b^2 \)
7. \( 3x(5 + x)^2 - x(3x - 6)^2 = 3x(25 + 10x + x^2) - x(9x^2 - 36x + 36) = (75x + 30x^2 + 3x^3) - (9x^3 - 36x^2 + 36x) = 75x + 30x^2 + 3x^3 - 9x^3 + 36x^2 - 36x = -6x^3 + 66x^2 + 39x \)

Ответ: 1) \( x^2 - 6x + 1 \); 2) \( -x^2 - 36 \); 3) \( 12ab + 9b^2 \); 4) \( 20x^2 + 4xy + 13y^2 \); 5) \( -13x + 25 \); 6) \( -26ab + 3b^2 \); 7) \( -6x^3 + 66x^2 + 39x \).