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<math>

We multiply <math>(a+1)(b+1)<math> to get <math>(ab+1+a+b)<math>

This makes the equation <math>(ab+1)(ab+1+a+b)+ab<math>

Now we seperate the equation to <math>(ab+1)(ab+1)+(ab+1)(a+b)+ab$ (Error compiling LaTeX. Unknown error_msg)

We get $(ab+1)^2 +(a+b)(ab+1)+ab<math>

Now this is just a quadratic equation

Thus we get a factored form of:

<math>(ab+1+a)(ab+1+b)$ (Error compiling LaTeX. Unknown error_msg)

That is the solution