Final answer:
In general, depth-first search does not always expand at least as many nodes as A* search with an admissible heuristic.
Step-by-step explanation:
In general, no, depth-first search (DFS) does not always expand at least as many nodes as A* search with an admissible heuristic.
Depth-first search explores a branch of the search tree as deeply as possible before backtracking. This can lead to a scenario where DFS explores a large number of nodes in a single branch before finding a solution, while A* search with an admissible heuristic is more guided and explores fewer nodes with potentially higher values.
However, it is important to note that the specific behavior of DFS and A* search can vary depending on the problem and the particular heuristics used. In some cases, DFS might explore more nodes than A* search, but this is not a general rule.