怎样简便计算20032002² ----------------------- 20032001²+20032003²-2

怎样简便计算20032002² ----------------------- 20032001²+20032003²-2
怎样简便计算20032002² ----------------------- 20032001²+20032003²-2

怎样简便计算20032002² ----------------------- 20032001²+20032003²-2
设20032002=A,则20032201=A-1,20032003=A+1,
原式=A²-(A-1)²+(A+1)²-2
=A²+4A-2
=A²+4A+4-6
=(A+2)²-6
=20032004²-6

设20032002=a，
则20032001=a-1,
20032003=a+1，
原式=a²-(a-1)²+(a+1)²-2
=a²+4a-2
=a²+4a+4-6
=(a+2)²-6
将a=20032002代入上式得：
(a+2)²-6=20032004²-6