3a^3-12a^2+12a
=3a(a^2-4a+4)
=3a(a-2)^2
-9-6ab-a^2b^2
=-(9+6ab+a^b^2)
=-(3+ab)^2
m^3n/4-m^2n^2/4+mn^3/16
=mn/16(4m^2-4mn+n^2)
=mn/16(2m-n)^2
a^4-2a^2+1
=(a^2-1)^2
=[(a+1)(a-1)]^2
=(a+1)^2(a-1)^2
(x-2y)^2-12(x-2y)+36
=(x-2y-6)^2
(a+2b)^2+2(a+2b)(2a+b)+(2a+b)^2
=[(a+2b)+(2a+b)]^2
=(3a+3b)^2
=9(a+b)^2