Question

因式分解：x^6-y^6+x^4+x^2y^2+y^4

Answer 1

^6-y^6+x^4+x^2y^2+y^4

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

=(x^2-y^2+1)(x^4+x^2y^2+y^4)

=(x^2-y^2+1)(x^4+2x^2y^2+y^4-x^2y^2)

=(x^2-y^2+1)[(x^2+y^2)^2-x^2y^2]

=(x^2-y^2+1)(x^2+y^2-xy)(x^2+y^2+xy)