We can say that A * Search is the best form of Best First Search. Also, avoids expensive expanding path. Although, first expands most promising path.
f(n) = g(n) + h(n), where
g(n) is the cost to reach the node
h(n), it is estimated cost to get from the node to the goal
f(n) it is defined as the estimated total cost of path through n to goal. Also, we will use priority queue by increasing f(n) to implement it.