In verse 29 the demon-possessed people address Jesus; here the demons themselves speak to him. This is the only place in the New Testament where this particular word for demon is used. Earlier Matthew used the more common word for demon (7.22), and in the following chapter he does so again (9.33-34). Elsewhere in the Gospel demons are mentioned in 10.8; 11.18; 12.24, 27, 28; and 17.18. Despite this fact, translators will normally use the same word they did in verse 28.
Begged, if not readily translated, can be “plead with” or “asked him fervently.”
If you cast us out is stated in such a way in Greek as to indicate that the demons were certain that Jesus was going to drive them out. It may therefore be rendered “Since you are going to cast us out” or “We know you’re going to cast us out.” For cast … out, see comments on verse 16 and on 7.22.
No reason is given why the demons requested that Jesus allow them to enter the herd of pigs. It may be that they needed some physical bodies from which to carry out their activities. However, the request of the demons was self-destructive, because the pigs rushed down the cliff into the lake and were drowned. The implication is that the demons were destroyed at the same time.
Quoted with permission from Newman, Barclay M. and Stine, Philip C. A Handbook on the Gospel of Matthew. (UBS Handbook Series). New York: UBS, 1988. For this and other handbooks for translators see here .
