1987 USAMO Problems/Problem 1

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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$. From this the two m^3 cancel and you get: <cmath>2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0</cmath> You can divide by$n$ (nonzero). You get: \[2n^2+m+m^2n+3m^2-3mn=0\]