Answer
$(x+y)^{2}(x+y+10)(x+y-10)$
Work Step by Step
$(x+y)^{4}- 100(x+y)^{2}$
Takeout common factor $(x+y)^{2}$
$=(x+y)^{2}((x+y)^{2}-100)$
$=(x+y)^{2}((x+y)^{2}-10^{2})$
Use the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$
$=(x+y)^{2}((x+y)+10)((x+y)-10)$
$=(x+y)^{2}(x+y+10)(x+y-10)$
