what's the easy way to create low poly background by adobe illustrator?

While I'm sure there are tools to assist with a technique like your desired look, I was having trouble finding them. :\

But I did find some good tutorials that may give you the insight you'd like.

• Vectorboom has a fairly straight forward one - http://vectorboom.com/load/tutorials/effects/polygonal_vector_mosaic/3-1-0-305 <-- this one assumes you are using some of the supporting code - always make sure you're getting code from a source you can trust or read it for yourself and make sure it's not doing anything weird.
• There is also a rather nice one from Connecting 4 - http://connecting4.com/how-to-adobe-illustrator-geometric-art/