Answer
$(x+y)(4a+5)(4a-5)$
Work Step by Step
$16a^{2}x-25y-25x+16a^{2}y$=
... Group the terms containing $b^{2}$ and factor in pairs
$=(16a^{2}x+16a^{2}y)+(-25y-25x)$
$=16a^{2}(x+y)-25(x+y)$
$=(x+y)(16a^{2}-25)$
...The second parentheses hold a difference of squares $(4a)^{2}-5^{5}$
= $(x+y)(4a+5)(4a-5)$
