5. Упростите: a) 0,5 (-4x-5)² - 8x (x + 1); б) (5а + 3) (а-2) - (2a - 7)².

Решение: a) $$0.5(-4x - 5)^2 - 8x(x + 1) = 0.5(16x^2 + 40x + 25) - 8x^2 - 8x = 8x^2 + 20x + 12.5 - 8x^2 - 8x = 12x + 12.5$$ б) $$(5a + 3)(a - 2) - (2a - 7)^2 = 5a^2 - 10a + 3a - 6 - (4a^2 - 28a + 49) = 5a^2 - 7a - 6 - 4a^2 + 28a - 49 = a^2 + 21a - 55$$