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

Problem

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:

$\boxed{(ab+1+a)(ab+1+b)}$