Answer
$(x-y)^2(x-y+2)(x-y-2)$
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: $(x-y)^4-4(x-y)^2=\\=((x-y)^2)^2-(2(x-y))^2\\=((x-y)^2+2(x-y))((x-y)^2-2(x-y))\\=(x-y)^2((x-y)+2)((x-y)-2)\\=(x-y)^2(x-y+2)(x-y-2)$
