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) $25 - m^2 - 12mn - 36n^2$

1) $81c^2 - d^2 + 9c + d = (81c^2 + 9c) - (d^2 - d) = 9c(9c + 1) - d(d-1)$ - не раскладывается на множители. $81c^2 - d^2 + 9c + d = (9c-d)(9c+d) + (9c+d) = (9c+d)(9c-d+1)$ 2) $a^2 + 8ab + 16b^2 - 1 = (a^2 + 8ab + 16b^2) - 1 = (a + 4b)^2 - 1 = (a + 4b - 1)(a + 4b + 1)$ 3) $ax^6 - 3x^6 - ax^3 + 3x^3 = x^6(a - 3) - x^3(a - 3) = (a - 3)(x^6 - x^3) = (a - 3)x^3(x^3 - 1) = (a - 3)x^3(x - 1)(x^2 + x + 1)$ 4) $25 - m^2 - 12mn - 36n^2 = 25 - (m^2 + 12mn + 36n^2) = 5^2 - (m + 6n)^2 = (5 - (m + 6n))(5 + (m + 6n)) = (5 - m - 6n)(5 + m + 6n)$