Упростите выражение: 1) (x - 2)(x - 11) - 2x(4 - 3x); 2) (a + 6)(a - 3) + (a - 4)(a + 5); 3) (y - 8)(2y - 1) - (3y + 1)(5y - 2); 4) (x + 2)2 - (x - 3)(x + 3); 5) (7a - 5b)(7a + 5b) - (4a + 7b)2; 6) (y - 2)(y + 3) - (y - 1)2 + (5 - y)(y + 5)
Решение:
(x - 2)(x - 11) - 2x(4 - 3x) = x^2 - 13x + 22 - 8x + 6x^2 = 7x^2 - 21x + 22.
(a + 6)(a - 3) + (a - 4)(a + 5) = a^2 - 3a + 6a - 18 + a^2 - 4a + 5a - 20 = 2a^2 + 4a - 38.
(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) = 2y^2 - 17y + 8 - 15y^2 + y + 2 = -13y^2 - 16y + 10.
(x + 2)^2 - (x - 3)(x + 3) = (x^2 + 4x + 4) - (x^2 - 9) = x^2 + 4x + 4 - x^2 + 9 = 13 + 4x.
(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.
(y - 2)(y + 3) - (y - 1)^2 + (5 - y)(y + 5) = (y^2 + 3y - 2y - 6) - (y^2 - 2y + 1) + (5y + 25 - y^2 - 5y) = y^2 + y - 6 - y^2 + 2y - 1 - y^2 + 5y - 5y + 25=- y^2+3y+18