(1)(x+y)^2-6x(x+y)+9x^2
=((x+y)-3x)^2
=(2x-y)^2
(2)a^2+2a(b+c)+(b+c)^2
=(a+(b+c))^2
=(a+b+c)^2
(3)-a^3+2a^2-a
=-a(a^2-2a+1)
=-a(a-1)^2
(4)4xy^2-4x^2y-y^3
=-y(4x^2-4xy+y^2)
=-y(2x-y)^2