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