to expand  - ampliarse, extenderse, expandir, dilatar, aumentar, ampliar, expandirse, dilatarse (dícese de los metales, gases, etc.), extender 

to extend  - extender, tender, extenderse, prolongar, prorrogar, agrandar, ampliar, aumentar, dar, ofrecer 

to widen  - ampliar, ensanchar, ampliarse, ensancharse 

to elaborate on