tag:blogger.com,1999:blog-2400513859305780710.post5235662641119931194..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Factor That! Topic: Factoring. Level: AMC/AIME/Olympiad.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2400513859305780710.post-27319537319228592892005-12-04T13:30:01.000-08:002005-12-04T13:30:01.000-08:00The second problem is pretty well-known:a^3 + b^3 ...The second problem is pretty well-known:<br><br>a^3 + b^3 + c^3 = (a + b + c)(a^2 + b^2 + c^2 - (a*b + b*c + a*c)).<br><br>It came in handy on a USAMTS problem last year, actually, because the <br>second term is always greater than or equal to zero.<br><br>Sorry for the double-post; I was sloppy and made a mistake on my first one (you can delete it).zanttrangnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-83352175367493117062006-02-27T21:16:26.000-08:002006-02-27T21:16:26.000-08:00[...] which is just Schur’s Inequality, so the res...[...] which is just Schur’s Inequality, so the result is proved. QED. [...]Mathematical Food for Thoughthttp://wangsblog.com/jeffrey/?p=93noreply@blogger.com