$$2009\times 2009-2008\times 2008=$$． 
Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula
$$=(2008+1)\times 2009-2008\times 2008$$  $$=2008\times 2009+2009-2008\times 2008$$  $$=2008\times (2009-2008)+2009$$  $$=2008+2009$$  $$=4017$$． 