Повторюємо алгебру за 8 клас: 18

18. Виконайте дію:

1) 3x(x - 1)9x2 - y2 + xy - yy2 - 9x2 = 3x(x - 1)9x2 - y2 – xy - y9x2 - y2 = 3x2 - 3x - xy + y9x2 - y2 = 3x(x - 1) - y(x - 1)(3x - y)(3x + y) = (3x - y)(x - 1)(3x - y)(3x + y) = x - 13x + y.

2) a - 5ab - a2 – 5 - bab - b2 = a - 5a(b - a) – 5 - bb(a - b) = 5 - a\ba(a - b) – 5 - b\ab(a- b) = 5b - ab - 5a + abab(a - b) = 5b - 5aab(a - b) = -5(a - b)ab(a - b) = –5ab;

3) x2 + x - 2x2 - 4 – 23x - 6 – 1 = x2 + x - 2(x - 2)(x + 2) – 2\x+23(x - 2) – 1\3(x2-4) = 3x2 + 3x - 6 - 2x - 4 - 3x2 + 123(x - 2)(x + 2) = x + 23(x- 2)(x + 2) = 13(x - 2) = 13x - 6;

4) m2 - 9a2 + 6a + 9 : 12 - 4map + 3p = (m - 3)(m + 3)(a + 3)2 • p(a + 3)4(3 - m) = –(m - 3)(m + 3) • p(a + 3) • 4(m - 3) = –p(m + 3)4(a + 3).