1) $$(x-2)(x-11) - 2x(4-3x) = x^2 - 11x - 2x + 22 - 8x + 6x^2 = 7x^2 - 21x - 8x + 22 = 7x^2 - 29x + 22$$
2) $$(a+6)(a-3) + (a-4)(a+5) = a^2 - 3a + 6a - 18 + a^2 + 5a - 4a - 20 = 2a^2 + 3a + a - 38 = 2a^2 + 4a - 38$$
3) $$(y-8)(2y-1) - (3y+1)(5y-2) = 2y^2 - y - 16y + 8 - (15y^2 - 6y + 5y - 2) = 2y^2 - 17y + 8 - 15y^2 + y + 2 = -13y^2 - 16y + 10$$
4) $$(x+2)^2 - (x-3)(x+3) = x^2 + 4x + 4 - (x^2 - 9) = x^2 + 4x + 4 - x^2 + 9 = 4x + 13$$
5) $$(7a-5b)(7a+5b) - (4a+7b)^2 = (49a^2 - 25b^2) - (16a^2 + 56ab + 49b^2) = 49a^2 - 25b^2 - 16a^2 - 56ab - 49b^2 = 33a^2 - 56ab - 74b^2$$
6) $$(y-2)(y+3) - (y-1)^2 + (5-y)(y+5) = y^2 + 3y - 2y - 6 - (y^2 - 2y + 1) + (25 - y^2) = y^2 + y - 6 - y^2 + 2y - 1 + 25 - y^2 = -y^2 + 3y + 18$$