x4+(x+y)4+y4分解因式

Question

x4+(x+y)4+y4 分解因式

Answer 1

x^4+(x+y)^4+y^4
=(x^2+y^2)^2-2x^2y^2+(x+y)^4
=[(x+y)^2-2xy]^2-2x^2y^2+(x+y)^4
=[(x+y)^2]^2-4xy(x+y)^2+4x^2y^2-2x^2y^2+(x+y)^4
=2(x+y)^4-4xy(x+y)^2+2x^2y^2
=2[(x+y)^4-2xy(x+y)^2+(xy)^2]
=2[(x+y)^2-xy]^2
=2(x^2+xy+y^2)^2