AoPS Wiki talk:Problem of the Day/June 29, 2011

Solution

This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.

First we have the question: (ab+1)(a+1)(b+1)+ab

We multiply (a+1)(b+1) to get (ab+1+a+b)

This makes the equation (ab+1)(ab+1+a+b)+ab

Now we seperate the equation to (ab+1)(ab+1)+(ab+1)(a+b)+ab

We get (ab+1)^2 +(a+b)(ab+1)+ab

Now this is just a quadratic equation

Thus we get a factored form of:

(ab+1+a)(ab+1+b)

That is the solution