1. 6a^3 - 6a = 6a(a^2 - 1) = 6a(a - 1)(a + 1)
2. 5a^2 + 10ab + 5b^2 = 5(a^2 + 2ab + b^2) = 5(a + b)^2
3. -8a^5 + 8a^3 - 2a = -2a(4a^4 - 4a^2 + 1) = -2a(2a - 1)^2
4. 1/9 - 3x^2 = (1/3 - √3 x)(1/3 +√3 x)
5. x + 5y + x^2 - 25y^2 = (x + x^2) + (5y - 25y^2) = x(x + 1) + 5y(1 - 5y)
6. 9 - c^2 + a^2 - 6a = (9 - c^2) + (a^2 - 6a) = (3 - c)(3 + c) + a(a - 6)