1987 USAMO Problems/Problem 1
Revision as of 11:17, 20 December 2015 by Bassmaster (talk | contribs)
By expanding you get ![\[m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3\]](http://latex.artofproblemsolving.com/0/d/1/0d1544ffb34dff29d0aa0c0d362cbe0b13b1a430.png)
From this the two 
cancel and you get:
![\[2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0\]](http://latex.artofproblemsolving.com/4/2/8/4280b7e66e77cbcafd88221eac9fe0f393490077.png)
You can divide by 
(nonzero).
You get:
![\[2n^2+m+m^2n+3m^2-3mn=0\]](http://latex.artofproblemsolving.com/9/8/9/98978fc9b2412fa469ad1a9a34ac576da4625162.png)
You can now factor the equation into:
![\[2n^2+(m^2-3m)n+(3m^2+m)=0\]](http://latex.artofproblemsolving.com/9/7/5/975eb800f6268d629e943923140e0a35c9af5afe.png)
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