Повторюємо алгебру за 8 клас: 17

17. Виконайте дію:

1) 2a2 - 2a4a2 - b2 + b(a - 1)b2 - 4a2 = 2a2 - 2a4a2 - b2 – b(a - 1)4a2 - b2 = 2a(a - 1) - b(a - 1)4a2 - b2 = (a - 1)(2a- b)(2a - b)(2a + b) = a - 12a + b;

2) x + 3xy - x2 + y + 3xy - y2 = x + 3x(y - x) + y + 3y(x - y) = x + 3\yx(y - x) – y + 3\xy(y - x) = xy + 3y - xy - 3xxy(y - x) = -3(x - y)xy(y - x) = -3(x - y)-xy(x - y) = 3xy;

3) x2 + x - 3x2 - 9 – 32x - 6 – 1 = x2 + x - 3\2(x - 3)(x + 3) – 3\x + 32(x - 3) 1\2(x2-9) = 2x2 + 2x - 6 - 3x - 9 - 2x2 + 182(x - 3)(x + 3) = -x + 32(x - 3)(x + 3) = -(x - 3)2(x - 3)(x + 3) = –12(x + 3);

4) ax - 2x3y + 6 : 4 - a2y2 - 4y + 4 = x(a - 2)3(y + 2) • (y + 2)2(2 + a)(2 + a) = –x(a - 2)(y + 2)3(a - 2)(a + 2) = –x(y + 2)3(a + 2).