Collocations for explore - verb

be keen to (esp. BrE), want to, wish to
be free to
In the afternoon you'll be free to explore a little on your own.

for
companies exploring for oil

extensively
briefly
fully, thoroughly
These questions have not been fully explored yet.

properly, systematically
carefully, deeply (esp. AmE), in detail
This idea is worth exploring in some detail.

further
usefully
The movie usefully explores some of the issues surrounding adoption.

need to
be keen to (esp. BrE), want to, wish to
aim to, seek to
begin to, continue to

Explore is used with these nouns as the subject:
article, artist, chapter, essay, exhibit, paper, research, researcher, study

Explore is used with these nouns as the object:
alternative, area, aspect, avenue, cave, complexity, concept, connection, consequence, delight, difference, dimension, effect, environment, extent, feasibility, frontier, galaxy, heritage, idea, impact, implication, influence, issue, limit, link, meaning, moon, mystery, myth, nature, neighbourhood, ocean, paradox, perception, possibility, potential, problem, question, reach, reason, region, relation, relationship, relevance, role, root, sexuality, strategy, subject, terrain, territory, theme, topic, unknown, way, wilderness, wonder, workings, world, wreck