Suppose that a is an integer such that
x^2+2xy−360y^2+ax+38y+361 can be factorized as the product of linear expressions in x and y. What is the value of a ?
The 2xy is a dead giveaway, since 360 = 18*20. So, we will need
(x+20y)(x-18y)
Now, since we have 361=19^2, we will have 19 in each linear factor
(x+20y+19)(x-18y+19) = x^2+2xy−360y^2+38x+38y+361
so, x=38