4a^2+4a-4a^2b+b+1
=4a^2+4a+1-4a^2b+b
=(2a+1)^2-b(4a^2-1)
=(2a+1)^2-b(2a-1)(2a+1)
=(2a+1)[(2a+1)-b(2a-1)]
=(2a+1)(2a+1-2ab+b)