펼치다 is opening something out flat — a book, a map, a folded item (이걸 이렇게 펼쳐서 찍으니까) — or, by extension, laying out plans and putting on a show: 화려하게 펼치는 걸 한번 보여드리겠습니다 (I'll show you a flashy display of it). -게 supplies the manner. Its passive twin 펼쳐지다 is used when the thing simply lies spread out with nobody doing it.