a^3-a
=a(a^2-1)
=a(a+1)(a-1)
a^2-4a+4-c^2
=(a^2-4a+4)-c^2
=(a-2)^2-c^2
=(a+c-2)(a-c-2)
(a+b)^4-6(a+b)^3+9(a+b)^2
=(a+b)^[2(a+b)^2-6(a+b)+9]
=(a+b)^2(a+b-3)^2