When multiply a binomial and trinomial it is sort of like distributing the 2x and the y to the terms in the trinomial. Make sure to keep your signs in check though! It should look something like this:
(2x + y)(5x - y + 3)
(10x^2 - 2xy + 6y) + (5xy - y^2 + 3y)
Combine like terms like always
10x^2 + 3xy + 9y - y^2
Hope this helps!