15. Запишите выражения в виде многочлена:

Решение:

1. \((x-6)^2 - x(x+8) = x^2 - 12x + 36 - x^2 - 8x = -20x + 36\)
2. \(9x(x+6) - (3x+1)^2 = 9x^2 + 54x - (9x^2 + 6x + 1) = 9x^2 + 54x - 9x^2 - 6x - 1 = 48x - 1\)
3. \(y(y-1) - (y-5)^2 = y^2 - y - (y^2 - 10y + 25) = y^2 - y - y^2 + 10y - 25 = 9y - 25\)
4. \(16y(2-y) + (4y-5)^2 = 32y - 16y^2 + 16y^2 - 40y + 25 = -8y + 25\)
5. \((x-5)^2 - x^2 = x^2 - 10x + 25 - x^2 = -10x + 25\)
6. \((2y+1)^2 - 4y^2 = 4y^2 + 4y + 1 - 4y^2 = 4y + 1\)
7. \(9x^2 - 1 - (3x-2)^2 = 9x^2 - 1 - (9x^2 - 12x + 4) = 9x^2 - 1 - 9x^2 + 12x - 4 = 12x - 5\)
8. \(x + (5x+2)^2 = x + 25x^2 + 20x + 4 = 25x^2 + 21x + 4\)

Ответ: 1) -20x + 36; 2) 48x - 1; 3) 9y - 25; 4) -8y + 25; 5) -10x + 25; 6) 4y + 1; 7) 12x - 5; 8) 25x^2 + 21x + 4.