1.(x^2+2x-2)(x^2+2x+4)+9
=(x^2+2x)^2+2(x^2+2x)+1
=(x^2+2x+1)^2
=(x+1)^4
2.(a^2-1)^2+30(1-a^2)+225
=(a^2-1)^2-30(a^2-1)+225
=(a^2-1-15)^2
=[(a+1)(a-1)]^2
3.(x-y)^2+4(x^2-y^2)+4(x+y)^2
=(x-y)^2+4(x-y)(x+y)+4(x+y)^2
=(x-y+2x+2y)^2
=(3x+y)^2