2022年人教版八年级上册整式的乘法与因式分解教案 .pdf

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1、精品教学教案人教版八年级上册整式的乘法与因式分解教案一、教学内容及授课目的教学内容：（1）整式的加减（2）整式的乘法（3）乘法公式与整式的除法（4）因式分解教学目标：（1）掌握单项式与多项式的加减，并能够熟练对整式进行化简；（2）熟练运用整式的乘除法公式，掌握整式乘除法的运算步骤（3）正确理解因式分解的意义，熟练十字相乘法的应用，能够将其应用在因式分解中。重 难 点：1.整式的乘除法与公式的应用 2用十字相乘等方法将题目进行因式分解二、授课提纲整式的加减整式的乘法、除法因式分解教学步骤及内容：一、知识点回归整式的乘除：1、合并同类项：把多项式中的同类项 合并成一项，叫做合并同类项.例如：_3a

2、a；_22aa；_8253baba_210242333222xxyxyxxyxyyx2、同底数幂的乘法法则：am an=am+n(m，n 是正整数).同底数幂相乘，底数不变，指数相加.例如：_3aa；_32aaa3、幂的乘方法则：(am)n=amn(m，n 是正整数).幂的乘方，底数不变，指数相乘.例如：_)(32a；_)(25x；()334)()(aa知识网络精品教学教案4、积的乘方的法则：(ab)m=ambm(m 是正整数).积的乘方，等于把积的每一个因式分别乘方，再把所得的幂相乘.例如：_)(3ab；_)2(32ba；_)5(223ba5、同底数幂的除法法则：am an=am-n(a0，

3、m，n 都是正整数，并且m n).同底数幂相除，底数不变，指数相减.规定：10a例如：_3aa；_210aa；_55aa6、单项式乘法法则单项式与单项式相乘，把它们的系数、相同字母的幂分别相乘，其余字母连同它的指数不变，作为 积的因式。yx 32)5)(2(22xyyx)2()3(22xyxy2232)()(baba7、单项式除法法则单项式相除，把系数与同底数幂分别相除作为商的因式，对于只在被除式里含有的字母，则连同它的指数作为商的一个因式.yxyx2324xyyx6242581031068、单项式与多项式相乘的乘法法则：单项式与多项式相乘，就是用单项式去乘多项式的每一项，再把所得的积相加.)

4、(cbam)532(2yxx)25(32babaab9、多项式乘法法则：多项式与多项式相乘，先用一个多项式的每一项乘另一个多项式的每一项，再把所得的积相加.文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8

5、R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 H

6、Y3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y1

7、0U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6

8、ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L

9、10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9

10、文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9精品教学教案

11、)6)(2(xx)12)(32(yxyx)(22bababa10、多项式除以单项式的除法法则：多项式除以单项式，先把这个多项式的每一项除以 这个单项式，再把所得的商相加.xxxy56；aaba4482bababa232454520ccbca212122211、整式乘法的平方差公式：(a+b)(a-b)=a2-b2.两个数的和与这两个数的差的积，等于这两个数的平方差.例如：（4a1）（4a+1）=_；（3a2b）（2b+3a）=_；11 mnmn=；)3)(3(xx；12、整式乘法的完全平方公式：(a+b)2=a2+2ab+b2，(a-b)2=a2-2 ab+b2.两数和(或差)的平方，等于它们

12、的平方和，加(或减)它们的积的2 倍.例如：_522ba；_32yx_22ab；_122m二、因式分解：1、提公共因式法（1）、如果一个多项式的各项含有公因式,那么就可以把这个公因式提出来,从而将多项式化成 两个因式乘积的形式.这种分解因式的方法叫做提公因式法.如:ab aca（bc）（2）、概念内涵:因式分解的最后结果应当是“积”;公因式可能是单项式,也可能是 多项式;提公因式法的理论依据是乘法对加法的分配律,即:mamb-mc=m(a b-c)文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU

13、4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10

14、X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档

15、编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9

16、N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9

17、T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3

18、Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U

19、2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9精品教学教案练习4yxy32xxx2+12x3+4x)1()1(anam2、公式法.：（1）、平方差公式：)(22bababa12x2294ba22)(16zyx22)2()2(baba（2）、完全平方公式：222)(2bababa222)(2bababa442mm2269yxyx924162xx36)(12)(2

20、baba3、分组 分解法：如:)()()(nmbanmbnmabnbmanam（2）、概念内涵:分组分解法的关键是如何分组,要尝试通过分组后是否有公因式可提,并且可继续 分解,分组后是否可利用公式法继续分解因式.（3）、注意:分组时要 注意符号的变化.1abababcbaca22abb2c24、“十字相乘法”：文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 H

21、Y3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y1

22、0U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6

23、ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L

24、10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9

25、文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:C

26、R9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8

27、R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9精品教学教案即式子 x2+(p+q)x+pq的因式分解.x2+(p+q)x+pq=(x+p)(x+q).有些二次三项式，可以把第一项和第三项的系数分别分解为两个数之积，然后借助画十字交叉线的方法，把二次三项式进行因式分解，这种方法叫十字相乘法。简单的说十字相乘法就是：十字左边相乘等于二次项系数，右边相乘等于常数项，交叉相乘再相加等于一次项系数。注意：十字相乘法不是适合所有二次三项式，只有在一次项系数和二次项系数以及常数项存在一种特殊关系时才能用，这个特

28、殊关系我们通过例题来说明：例：分解267xxx2 7x6（2）、x25x 6（3）、x25x6 文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9

29、文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:C

30、R9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8

31、R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 H

32、Y3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y1

33、0U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9文档编码:CR9N5Z8R9T7 HY3Z1Y10U2G6 ZU4I7L10X2M9