Разложите на множители: а) 81c^2 - d^2 + 9c + d б) a^2 + 8ab + 16 b^2 - 1 в) ax^6 - 3x^6 - ax ^3 + 3x^3 г) 25 - m^2 - 12 mn - 36n^2

а) 81c^2 - d^2 + 9c + d = (81c^2 - d^2) + (9c + d) = ((9c) ^2 - d^2) + (9c + d) = (9c - d) (9c + d) + (9c + d) = (9c + d) ((9c - d) + 1) = (9c + d) (9c - d + 1)

Ответ: (9c + d) (9c - d + 1).

б) a^2 + 8ab + 16b^2 - 1 = (a^2 + 8ab + 16b^2) - 1 = (a^2 + 2 * 4ab + (4b) ^2) - 1 = (a + 4b) ^2 - 1 = (a + 4b) ^2 - 1^2 = ((a + 4b) - 1) ((a + 4b) + 1) = (a + 4b - 1) (a + 4b + 1)

Ответ: (a + 4b - 1) (a + 4b + 1).

в) ax^6 - 3x^6 - ax^3 + 3x^3 = x^3 (ax^2 - 3x^2 - a + 3) = x^3 (x^2 (a - 3) - a + 3) = x^3 (x^2 (a - 3) + (-a + 3)) = x^3 (x^2 (a - 3) - (a - 3)) = x^3 (a - 3) (x^2 - 1) = x^3 (a - 3) (x - 1) (x + 1)

Ответ: x^3 (a - 3) (x - 1) (x + 1).

г) 25 - m^2 - 12mn - 36n^2 = 25 + (-m^2 - 12mn - 36n^2) = 25 - (m^2 + 12mn + 36n^2) = 25 - (m^2 + 2 * 6mn + (6n) ^2) = 25 - (m + 6n) ^2 = 5^2 - (m + 6n) ^2 = (5 - (m + 6n)) (5 + (m + 6n)) = (5 - m - 6n) (5 + m + 6n)

Ответ: (5 - m - 6n) (5 + m + 6n).