把(x+y)^4+(x^2-y^2)^2+(x-y)^4这个式子分解因式,把过程写给我

把(x+y)^4+(x^2-y^2)^2+(x-y)^4这个式子分解因式,把过程写给我
把(x+y)^4+(x^2-y^2)^2+(x-y)^4这个式子分解因式,把过程写给我

把(x+y)^4+(x^2-y^2)^2+(x-y)^4这个式子分解因式,把过程写给我
原式=(x+y)^4+(x+y)^2(x-y)^2+(x-y)^4
=(x+y)^4+2(x+y)^2(x-y)^2+(x-y)^4-(x+y)^2(x-y)^2
=[(x+y)^2+(x-y)^2]^2-(x^2-y^2)^2
=(2x^2+2y^2)^2-(x^2-y^2)^2
=[(2x^2+2y^2)+(x^2-y^2)][(2x^2+2y^2)-(x^2-y^2)]
=(3x^2+y^2)(x^2+3y^2)