In July, Microsoft and Facebook had made a search and advertisement deal, which meant that Live Search would be integrated into Facebook, along with advertisements. Well, the search has finally started to appear in Facebook now.
When you start typing in the search bar at the top right of your homepage, you'll notice a 'Search the Web' option. This is a very clever placement for Live Search, and I expect this to work in favor for Microsoft's search efforts. The search results are displayed in native Facebook style search results. Related text ads for the search results are shown at the right, showing how the new layout has been thought out well for monetary benefits by Facebook. The search results are provided by Live Search but directly open the search results upon clicking. Notice there is also a link for advanced search.
The search is also accessible from the All Results page, through the Web link.
Link: Redmond Pie