4x^3y+4x^2y^2+xy^3
=xy(4x^2+4xy+y^2)
=xy(2x+y)^2
a^2+4a(a+b)+4(a+b)^2
=a^2+4a(a+b)+[2(a+b)]^2
=(a+2a+2b)^2
=(3a+2b)^2
x^2-12
=x^2-(2√3)^2
=(x-2√3)(x+2√3).