因式分解题 x的4次方加上(x+y)的4次方加上y的4次方

x^4+(x+y)^4+y^4
=x^4+y^4+2x^2y^2-x^2y^2+(x^2+2xy+y^2)^2-x^2y^2
=(x^2+y^2)^2-x^2y^2+(x^2+2xy+y^2+xy)(x^2+2xy+y^2-xy)
=(x^2+y^2+xy)(x^2+y^2-xy)+(x^2+3xy+y^2)(x^2+xy+y^2)
=(x^2+xy+y^2)(2x^+2xy+2y^2)
=2(x^2+xy+y^2)^2

x^4+(x+y)^4+y^4
=2x^4+4x^3y+6x^2y^2+4xy^3+2y^4
=2(x^4+2x^3y+3x^2y^2+2xy^3+y^4)
=2[(x^4+x^3y+x^2y^2)+(x^3y+x^2y^2+xy^3)+(x^2y^2+xy^3+y^4)]
=2(x^2+xy+y^2)^2.

2(x*2+xy+y*2)*2
(注：*为平方）