Упростите выражение:
1) (a − 2)(a − 1) − a(a + 1);
2) (b − 5)(b + 10) + (b + 6)(b − 8);
3) (2c + 3)(3c + 2) − (2c + 7)(2c − 7);
4) (3d + 5)(5d − 1) − (6d − 3)(2 − 8d).
$(a - 2)(a - 1) - a(a + 1) = a^2 - 2a - a + 2 - a^2 - a = (a^2 - a^2) + (-2a - a - a) + 2 = 0 - 4a + 2 = -4a + 2$
$(b - 5)(b + 10) + (b + 6)(b - 8) = b^2 - 5b + 10b - 50 + b^2 + 6b - 8b - 48 = (b^2 + b^2) + (-5b + 10b + 6b - 8b) + (-50 - 48) = 2b^2 + 3b - 98$
$(2c + 3)(3c + 2) - (2c + 7)(2c - 7) = 6c^2 + 9c + 4c + 6 - (4c^4 + 14c - 14c - 49) = 6c^2 + 9c + 4c + 6 - 4c^4 - 14c + 14c + 49 = (6c^2 - 4c^4) + (9c + 4c - 14c + 14c) + (6 + 49) = 2c^2 + 13c + 55$
$(3d + 5)(5d - 1) - (6d - 3)(2 - 8d) = 15d^2 + 25d - 3d - 5 - (12d - 6 - 48d^2 + 24d) = 15d^2 + 25d - 3d - 5 - 12d + 6 + 48d^2 - 24d = (15d^2 + 48d^2) + (25d - 3d - 12d - 24d) - 5 + 6 = 63d^2 - 14d + 1$
Пожауйста, оцените решение
