Brain Teaser: Why does this trick work?

Start with any set of numbers. To be specific I will use the following numbers: 2 3 5 7 10.

Choose any two numbers and replace them with the number you get by adding their product and sum. For example, if you choose 2 and 3, replace them with (2*3)+(2+3)=11. Now choose two other numbers on the list and keep repeating the process until there is one number left. Your final number will be 6335.

Obviously this works because the order the numbers are chosen makes no difference. But why should that be? This problem is a fairly simple demonstration of an important mathematical technique.