1. 1) (x+4)(3x-2) = 3x^2 + 12x - 2x - 8 = 3x^2 + 10x - 8
2) (6m+5n)(7m-3n) = 42m^2+35mn-18mn-15n^2 = 42m^2+17mn-15n^2
3) (x+5)(x^2+x-6) = x^3+5x^2+x^2+5x-6x-30 = x^3+6x^2-x-30
2. 1) 7b(2b+3) - (b+6)(b-5) = 14b^2+21b - (b^2+b-30) = 13b^2+20b+30
2) (x+5)^2 - (x-4)(x+4) + (x-3)(x+7) = x^2+10x+25 - (x^2-16) + x^2+4x-21 =
= 10x + 41 + x^2 + 4x - 21 = x^2 + 15x + 20
3. 1) (3x+4)(4x-3) - 36 = (2x+5)(6x-7)
12x^2+16x-9x-12 - 36 = 12x^2+30x-14x-35
7x - 48 = 16x - 35
35 - 48 = 16x - 7x
-13 = 9x; x = -13/9
2) 4(3y+1)^2 - 27 = (4y+9)(4y-9) + 2(5y+2)(2y-7)
4(9y^2+6y+1) - 27 = 16y^2-81 + 2(10y^2-31y-14)
36y^2+24y+4-27 = 16y^2-81 + 20y^2-62y-28
24y - 23 = -62y - 109
24y + 62y = 23 - 109
86y = -86; y = -1
4. 4 последовательных натуральных числа: (x-1), x, (x+1), (x+2)
По условию
(x-1)(x+1) + 31 = x(x+2)
x^2 - 1 + 31 = x^2 + 2x
2x = 30; x = 15.
Ответ: 14, 15, 16, 17.