Dividing the appropriate polynomial expressions into the products is a basic part of the algorithm for reducing the number of computational operations in the analytical expressions of the robotic mechanisms dynamic models. On the basis of the mathematical background, the data structures and algorithm for dividing these polynomial expressions are developed. The central topic of the paper is the algorithm for choosing the products which give the largest reduction in the number of computational operations. From all generated products, that one is chosen which gives "maximal" reduction in the number of operations. Then, from all other products, the chosen addends are eliminated and the same procedure is repeated. The procedure stops when there is no product left to be chosen.