利用简便算法计算2009³-2008×2009×2010

问题描述:

利用简便算法计算2009³-2008×2009×2010

2009(2009^2-2009^2+1)=2009

2009³-2008×2009×2010
=2009³-(2009-1)×2009×(2009+1)
=2009³-2009X(2009^2-1)
=2009³-2009³+1
=1

2009³-2008×2009×2010
=2009³-(2009-1)×2009×(2009+1)
=2009³-2009X(2009²-1)
=2009³-2009³+2009
=2009

20级算错了
答案是2009