Answer
$(x+y)^{2}(x+y-10)(x+y+10)$
Work Step by Step
$(x+y)^{4}-100(x+y)^{2}=\quad$... factor out $(x+y)^{2}$
$=(x+y)^{2}((x+y)^{2}-100)$
... the brackets hold a difference of squares
$=(x-y)^{2}[(x+y)-10]\cdot[(x+y)+10]$
$=(x+y)^{2}(x+y-10)(x+y+10)$
