Let us consider the price of a cube shaped stone of edge length L inches. The cost of the raw stone is proportional to its weight which is proportional to cube of its length, i.e. L*L*L or L^3 (read "L cubed") . Assuming that it cost $1000 for one cubic inch of raw stone, we can write the cost of one raw stone as 1000L^3. Let cost of polishing a square inch of the surface area of the rock is $100. Noting that the surface area of rock is proportional to the square of length, i.e. L^2 (read "L squared") we have the cost of polishing the stone as 600L^2 (note there are 6 faces to a cube).

1. Assuming there is no other cost, write down an expression for the cost of the finished stone and identify the different terms in it.

2. What are the factors for each of these terms? Are there any factors common to these terms here?