2010的3次方-2009×2010×2011
问题描述：
2010的3次方-2009×2010×2011
答
2010^3-2009×2010×2011
=2010^3-2009×2011×2010
=2010^3-(2010-1)×(2010+1)×2010
=2010^3-(2010^2-1)×2010
=2010^3-(2010^3-2010)
=2010^3-2010^3+2010
=2010(2-1)(2+1)(2ˇ2+1)(2ˇ4+1)(2ˇ8+1)……(2ˇ64+1)(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^64+1) =(2^2-1)(2^2+1)(2^4+1)(2^8+1)……(2^64+1) =(2^4-1)(2^4+1)(2^8+1)……(2^64+1) =(2^8-1)(2^8+1)……(2^64+1) =(2^16-1)……(2^64+1) ........ =(2^64-1)(2^64+1) =2^128-1