1987 USAMO Problems/Problem 1
By expanding you get $$ (Error compiling LaTeX. Unknown error_msg)m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3
From this the two m^3 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)
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