  In this paper, we devote to extending structures for dendriform algebras.
First, we define extending datums and unified products of dendriform algebras,
and theoretically solve the extending structure problem. As an application, we
consider flag datums as a special case of extending structures, and give an
example of the extending structure problem. Second, we introduce matched pairs
and bicrossed products of dendriform algebras and theoretically solve the
factorization problem for dendriform algebras. Moreover, we also introduce
cocycle semidirect products and nonabelian semidirect products as special cases
of unified products. Finally, we define the deformation map on a dendriform
extending structure (more general case), not necessary a matched pair, which is
more practical in the classifying complements problem.
