奥数题 周期

Question

问题：1 321321×123减123123×321 2 369×135135135减369369369×135 3 1995×1995减1994×1994

Answer 1

321321×123减123123×321
=(321*1000+321)*123-(123*1000+123）*321
=321*123*1000+321*123-123*321*1000-123*321
=0

369×135135135减369369369×135
=369*（135*1000000+135*1000+135）-（369*1000000+369*1000+369）*135
=0

1995*1995-1994*1994
=（1994+1)*1995-1994*1994
=1994*1995-1994*1994+1995
=1994+1995
=2000+2000-6-5
=3989

Answer 2

1 .321321×123减123123×321
=321 ×101×123-123×101×321
=0.
2 . 369×135135135-369369369×135
=369 ×135×10101-369×10101×135
=0.
3 1995×1995减1994×1994
=(1995+1994)(1995-1994)
=3989.
或， 3 1995×1995减1994×1994 =1995×（1994+1）-1994×（1995-1）
=1995×1994+1995-1994×1995+1994=3989

Answer 3

321321×123-123123×321
=321*1001*123-123*1001*321
=0

369×135135135-369369369×135
=369*135*1001001-369*1001001*135
=0

1995×1995-1994×1994
=1995*(1994+1)-1994*(1995-1)
=1995*1994+1995-1994*195+1994
=1995+1994
=3989

Answer 4

1、321321×123-123123×321=321*1001*123-123*1001*321=0

2、369×135135135-369369369×135=369*135*1001001-369*1001001*135=0

3、1995×1995-1994×1994 =（1995+1994）*（1995-1994）=3989 这运用的是平方差公式

Answer 5

1.
321321×123-123123×321
=1001*321*123-1001*123*321
=0

2.
369×135135135减369369369×135
=369*1001001*135-1001001*369*135
=0

3.
1995×1995减1994×1994
=(1995-1994)(1995+1994)
=3989