Answer
Fill the blank with$\quad -2y$
Work Step by Step
With the foil method, with m and n being integers, we find that
$(x+m)(x+n)=x^{2}+(m+n)x+ mn,$
so ,the sum of mn is the coefficient of x, and
m and n are factors of the constant term.
Reversing, when we want to factor $x^{2}+bx+c,$ we search for two integers, m and n such that
their sum is b,
their product is c.
---
Here, we are given $b=-10y, c=16y^{2}$ ,
and one of the integers is m=$-8y$.
The other must be n=$-2y$, since
$(-8y)\cdot(-2y)=+16y^{2},\quad (-8y)+(-2y)=-10y$
Fill the blank with$\quad -2y$
