Вариант 3. Задание 3. Разложите на множители: 1) (a^2 - 36b^2 + a - 6b); 2) (25x^2 - 10xy + y^2 - 9); 3) (ay^7 + y^7 - ay^3 - y^3); 4) (4 - m^2 + 14mn - 49n^2).

**Решение:** 1) (a^2 - 36b^2 + a - 6b = (a - 6b)(a + 6b) + (a - 6b) = (a - 6b)(a + 6b + 1)) 2) (25x^2 - 10xy + y^2 - 9 = (5x - y)^2 - 3^2 = (5x - y - 3)(5x - y + 3)) 3) (ay^7 + y^7 - ay^3 - y^3 = y^7(a + 1) - y^3(a + 1) = (a + 1)(y^7 - y^3) = y^3(a + 1)(y^4 - 1) = y^3(a + 1)(y^2 - 1)(y^2 + 1) = y^3(a + 1)(y - 1)(y + 1)(y^2 + 1)) 4) (4 - m^2 + 14mn - 49n^2 = 4 - (m^2 - 14mn + 49n^2) = 2^2 - (m - 7n)^2 = (2 - (m - 7n))(2 + (m - 7n)) = (2 - m + 7n)(2 + m - 7n))