Вариант 4. Задание 3. Разложите на множители: 1) (81c^2 - d^2 + 9c + d); 2) (a^2 + 8ab + 16b^2 - 1); 3) (ax^6 - 3x^6 - ax^3 + 3x^3); 4) (25 - m^2 - 12mn - 36n^2).

**Решение:** 1) (81c^2 - d^2 + 9c + d = (9c - d)(9c + d) + (9c + d) = (9c + d)(9c - d + 1)) 2) (a^2 + 8ab + 16b^2 - 1 = (a + 4b)^2 - 1^2 = (a + 4b - 1)(a + 4b + 1)) 3) (ax^6 - 3x^6 - ax^3 + 3x^3 = x^6(a - 3) - x^3(a - 3) = (a - 3)(x^6 - x^3) = x^3(a - 3)(x^3 - 1) = x^3(a - 3)(x - 1)(x^2 + x + 1)) 4) (25 - m^2 - 12mn - 36n^2 = 25 - (m^2 + 12mn + 36n^2) = 5^2 - (m + 6n)^2 = (5 - (m + 6n))(5 + (m + 6n)) = (5 - m - 6n)(5 + m + 6n))