Answer
$(x+y)^2(x+y+10)(x+y-10)$
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: $(x+y)^4-100(x+y)^2=\\=((x+y)^2)^2-(10(x+y))^2\\=((x+y)^2+10(x+y))((x+y)^2-10(x+y))\\=(x+y)^2((x+y)+10)((x+y)-10)\\=(x+y)^2(x+y+10)(x+y-10)$
