A.T. Robertson Commentary Acts 11:4

"But Peter began, and expounded [the matter] unto them in order, saying," — Acts 11:4 (ASV)

Began (αρξαμενος). Not pleonastic here, but graphically showing how Peter began at the beginning and gave the full story of God's dealings with him in Joppa and Caesarea.

Expounded (εξετιθετο). Imperfect middle of εκτιθημ, to set forth, old verb, but in the N.T. only in Acts (7:21; 11:4; 18:26; 28:23), a deliberate and detailed narrative "in order" (καθεξης). Old word for in succession. In the N.T. only in Lu 1:2; 8:1; Acts 3:24; 11:14; 18:23. Luke evidently considered this defence of Peter important and he preserves the marks of authenticity. It came originally from Peter himself (verses 5,6,15,16). "The case of Cornelius was a test case of primary importance" (Page), "the first great difficulty of the early Church." Part of the story Luke gives three times (10:3-6,30-32; 11:13f.). See the discussion chapter 10 for details given here.