Упрости выражения.

Решение:

1. \( 8 - (y + 4)(y - 4) = 8 - (y^2 - 16) = 8 - y^2 + 16 = 24 - y^2 \)
2. \( (3b + 5c)(5c - 3b) + 9b^2 = (5c + 3b)(5c - 3b) + 9b^2 = (25c^2 - 9b^2) + 9b^2 = 25c^2 \)
3. \( 9x(2 - x) + (3x + 2)^2 = 18x - 9x^2 + (9x^2 + 12x + 4) = 18x - 9x^2 + 9x^2 + 12x + 4 = 30x + 4 \)
4. \( 4(x^2 + 4) - (5x - 4)^2 = 4x^2 + 16 - (25x^2 - 40x + 16) = 4x^2 + 16 - 25x^2 + 40x - 16 = -21x^2 + 40x \)
5. \( 3(x + y)^2 - 6xy = 3(x^2 + 2xy + y^2) - 6xy = 3x^2 + 6xy + 3y^2 - 6xy = 3x^2 + 3y^2 \)
6. \( (x - 3)^2 - (x + 3)(3 - x) = (x^2 - 6x + 9) - (-(x + 3)(x - 3)) = (x^2 - 6x + 9) - (-(x^2 - 9)) = x^2 - 6x + 9 + x^2 - 9 = 2x^2 - 6x \)

Ответ: 1. \( 24 - y^2 \); 2. \( 25c^2 \); 3. \( 30x + 4 \); 4. \( -21x^2 + 40x \); 5. \( 3x^2 + 3y^2 \); 6. \( 2x^2 - 6x \).