Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 29, 2011"
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==Solution== | ==Solution== | ||
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+ | 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 |
Revision as of 23:07, 28 June 2011
Problem
AoPSWiki: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