多项式乘以多项式教案.pdf

《多项式乘以多项式教案.pdf》由会员分享，可在线阅读，更多相关《多项式乘以多项式教案.pdf（5页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、名师精编优秀教案多项式乘以多项式教案高清华教学目标：知识与技能1、探索多项式与多项式相乘的乘法法则。2.能灵活地进行整式的乘法运算。过程与方法1、经历探索多项式与多项式相乘的乘法法则的过程，体会乘法分配律的作用以及“整体”和“转化”的数学思想；2、通过对乘法法则的探索，归纳与描述，发展有条理思考的能力和语言表达能力；情感、态度与价值观体验学习和把握数学问题的方法，树立学好数学的信心，培养学习数学的兴趣。教学重点：多项式的乘法法则及其应用。教学难点：探索多项式的乘法法则，灵活地进行整式的乘法运算。关键：多项式的乘法应先转化为单项式与多项式相乘进行运算，进一步转化为单项式的乘法，紧紧扣住这一线索。

2、教学方法：小组合作，自主学习教学过程：一、课前练习师：前面我们学习了整式的乘法，快速做一做，看看你掌握的怎样？名师精编优秀教案计算：2232)1(xyx)1(2)2(xxxxx24)3(xxx9)1944)(4(2生：交流答案师：同学们看这道题怎样做？)()5(bnam（多媒体展示）他和我们以前所学的有何不同？生：现在是多项式乘多项式师：那多项式乘多项式如何去计算呢？这节课我们一起来探究吧！二、学习目标（多媒体）师：看到这个课题你想学习哪些知识呢？生：交流师：（多媒体呈现）1、探究并了解多项式与多项式相乘的法则2、熟练的运用法则进行运算三、探求新知问题助学一：动手做一做：利用如下的长方形卡片拼

3、成更大的长方形（多媒体）(学生活动)小组内展评作品，推选出最优秀的同学的作品给全班学生展示。m a m b b n 文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2

4、I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X

5、2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M1

6、0Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4

7、U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ

8、7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4

9、M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3名师精编优秀教案你能用不同的方法表示此长方形的面积吗？生 1：(m+n)(a+b)生 2：ma+mb+na+nb 生 3：(m+n)a+(m+n)b

10、(m+n)(a+b)=(m+n)a+(m+n)b=ma+mb+na+nb 问题助学二：(多媒体)1、你能试着说说(m+b)(n+a)=m(n+a)+b(n+a)怎么来的吗？2、进一步完成 m(n+a)+b(n+a)的计算，并说说你的依据引导学生把其中一个因式ab 看作一个整体，再利用乘法分配律来理解mn 与 ab 相乘的结果，从而导出多项式与多项式相乘的法则。四、诊断指导归纳、小结多项式乘法法则(1)文字叙述：多项式与多项式相乘，先用一个多项式的每一项分别乘以另一个多项式的每一项，再把所得的积相加（2）用字母表示法则的形成是本节课的重点之一。在学生归纳法则的过程中，结合学生讨论的情况，播放法则

11、的形成动画，并在此过程中进行启发讲解，让学生明白两个“每一项”的含义。五、点拨提升第一关：(1)(1-x)(0.6-x)(2)(2x+y)(x-y)n m a b 文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T

12、5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q

13、6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1

14、L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D

15、7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y

16、1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2

17、I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3名师精编优秀教案设计意图：第一关，目的加强对公式的熟练运用，采用小组合作学习，即先自己动手做一做，再

18、小组讨论兵教兵。最后一起交流小组学习的收获和应该注意的问题。随后在课本随堂练习中做了两道题来检测学生小组学习的情况。第二关：（1）（a+3）（b+5）；（2）（3x-y）(2x+3y)；设计意图：第二关，题目的设置难度稍微加深，并设置了选做题（多媒体）。第三关：（1）(3x-2)(2x-3)(x+2)；（2）(a-b)(a+b)(a2+b2)第三关，小组竞赛，题目难度有所提升，目的是检测小组整体合作学习水平，并提高学生小组合作的意识。通过结果评选出优胜小组，奖励相应的分数。六、课堂小结1、多项式乘法是用“换元”的方法，将多项式与多项式相乘转化为单项式与多项式相乘。2、运用法则时，要有序地逐项相

19、乘，做到不重不漏。3、在含有多项式乘法的混合运算时，要注意运算顺序，计算结果要化简。七、课堂小测1、)(bxax 2、)1)(dcxbax3、2)32(x4、)2)(1()3)(2(yxyx选作题：已知22()()46,3()2xayxbyxxyyabab求代数式的值.八、板书设计多项式乘多项式文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1

20、 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文

21、档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5

22、C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6

23、C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L

24、3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7

25、T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1

26、Q6C1 ZR3F4U2I1L3名师精编优秀教案(m+b)(n+a)=mn+ma+bn+ba九、作业布置必做题：随堂练习1；选做题：配套练习册；自留作业文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ

27、4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR

28、3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码

29、:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3

30、HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1

31、ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3文档编码:CZ7X2D7T5C3 HQ4M10Y1Q6C1 ZR3F4U2I1L3