Answer
$(x+y)(x-y)(x+2y)(x-2y)$
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:
$x^4-5x^2y^2+4y^2=\\=x^4-x^2y^2-4x^2y^2+4y^2\\=x^2(x^2-y^2)-4y^2(x^2-y^2)\\=(x^2-y^2)(x^2+4y^2)\\=(x+y)(x-y)(x+2y)(x-2y)$
