Answer
$(x^2+y^2+xy)(x+y)(x-y)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $x^4-xy^3+x^3y-y^4=\\=(x^2)^2-(y^2)^2-xy(y^2-x^2)\\=(x^2+y^2)(x^2-y^2)+xy(x^2-y^2)\\=(x^2+y^2+xy)(x^2-y^2)\\=(x^2+y^2+xy)(x+y)(x-y)$