  In this paper we study some algebraic and combinatorial behaviors of
expansion functor. We show that on monomial ideals some properties like
polymatroidalness, weakly polymatroidalness and having linear quotients are
preserved under taking the expansion functor.
  The main part of the paper is devoted to study of toric ideals associated to
the expansion of subsets of monomials which are minimal with respect to
divisibility. It is shown that, for a given discrete polymatroid $P$, if toric
ideal of $P$ is generated by double swaps then toric ideal of any expansion of
$P$ has such a property. This result, in a special case, says that White's
conjecture is preserved under taking the expansion functor. Finally, the
construction of Gr\"{o}bner bases and some homological properties of toric
ideals associated to expansions of subsets of monomials is investigated.
