(x+y)^2+6(x+y)+9
=[(x+y)+3]^2
=(x+y+3)^2
a^2-2a(b+c)+(b+c)^2
=[a-(b+c)]^2
=(a-b-c)^2
4-12(x-y)+9(x-y)^2
=[2-3(x-y)]^2
=(2-3x+3y)^2
1-2x^2+x^4
=(1-x^2)^2
=(1+x)^2(1-x)^2
x^2-12xy+36y^2
=(x-6y)^2
25p^2+10pq+q^2
=(5p+q)^2