a: =x^2+2xy+y^2-4x^2y^2
=(x+y)^2-(2xy)^2
=(x+y-2xy)(x+y+2xy)
b: =(x^3-y^3)(x^3+y^3)
=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)
c: =25-(a^2-2ab+b^2)
=25-(a-b)^2
=(5-a+b)(5+a-b)
d: =(2bc-b^2-c^2+a^2)(2bc+b^2+c^2-a^2)
=[a^2-(b^2-2bc+c^2)][(b+c)^2-a^2]
=(a-b+c)(a+b-c)(b+c-a)(b+c+a)