2002×2003×2004-2000×2001×2002 简便预算

2002×2003×2004-2000×2001×2002
=2003(2003-1)(2003+1)-2001(2001-1)(2001+1)
=2003(2003^2-1)-2001(2001^2-1)
=2003^3-2003-2001^3+2001
=(2003^3-2001^3)-(2003-2001)
=(2003-2001)(2003^2+2001^2+2001*2003-1)
=2[(2002+1)^2+(2002-1)^2+(2002+1)(2002-1)-1]
=2(2002^2+2*2002+1+2002^2-2002+1+2002^2-1-1)
=6*2002^2
=6*(2000+2)^2
=6*(2000^2+2*2*2000+4)
=6*4008004
=24048024

原式=2002*（2003*2004-2000*2001)=2002*{(2000+3)*(2001+3)-2000*2001}
=2002*(2000*2001+3*2001+3*2000+9-2000*2001）
=2002*(3*2001+3*2000+9)
=2002*12012
=(2000+2)*12012
=24024000+24024
=24048024

原式=2002×{(2002+1)(2002+2)-(2002-1)(2002-2)}=2002×{(2002^2+3×2002+2)-(2002^2-3×2002+2)}=2002×(6×2002)=24048024

2002×2003×2004-2000×2001×2002
=2002(2003*2004-2000*2001)
=2002[2003*2004-2000(2003-2)]
=2002[2003*2004-2000*2003+2000*2]
=2002[2003(2004-2000)+2000*2]
=2002[2003*4+(2003-3)*2]
=2002[2003*4+2003*2-6]
=2002[2003(4+2)-6]
=2002(2003*6-6)
=2002*6(2003-1)
=2002*2002*6
=(2000+2)²×6
=4000000×6+2000×2×2×3+4×6
=24000000+24000+24
=24024024