2018年秋八年级数学上册第12章整式的乘除12.4整式的除法2多项式除以单项式导学课件新版华东师大版

12.4 整式的除法
目标二 能解决与多项式除以单项式有关的应用问题
例2 [教材补充例题] 校园里有一个长方形花坛的面积 12xy－4xy3)平方米，它的宽为6xy米，那么它的长为多
【解析】 利用长方形的面积公式，结合整式的除法运算法则求
解：∵这个长方形花坛的面积为(6x2y＋12xy－4xy3)平方米，它的 ∴它的长为(6x2y＋12xy－4xy3)÷6xy＝(x＋2－23y2)米． 答：这个长方形花坛的长为(x＋2－23y2)米．
反思
计算：(2m5－3m4－24m3)÷(－24m3)． 解：原式＝－m2＋m. (1)错因分析： (2)纠错
【答案】 (1)计算过程中漏掉了－24m3÷(－24m3)＝1这一项． (2)原式＝－m2＋m＋1.
Hale Waihona Puke 团Tiffany，a 16yearold girl，was very st September，her best friend，Sophie，moved abroad with her family because she had to continue her studies in America.She even said she would not come back for at least a few years. 1 “I was really sad the moment I heard the bad news and I didn't know what to do，” Tiffany recalled.“I shut myself in my room for a whole week.It was then that my aunt took me to a sports club one Saturday and I saw so many young people playing different kinds of sports there.I signed up for a beginner's course in volleyball and since then I have been playing this sport.Now I practice twice a week there.It is wonderful playing sports in this club and I have made lots of friends as well. 2 ” The most basic aim of playing sports is that you can improve your health even if you are not very good at sports.Besides，you can get to know a circle of people at your age while playing sports. 3 Since she joined the sports club，she has opened up herself and now she has become very active and enjoys meeting and talking with others. 1．It's polite for girls to kiss each other on the side of the face. 4．It's no big deal.For most people，that is one of the reasons why they join a sports club. 4 You don't have to sit down and talk to strangers.You go in for sports and it is easier to understand your partners on the same team.Now Tiffany is quite popular with her friends and she has also become more confident.团圆圆一家在台湾可受欢迎了 。每天 ，小朋 友们排 着长队 ，等着 跟它们 合影留 念。从 “排着 长队” 体现出 每天喜 欢它们 的人不 计其数 ，特别 受欢迎 。从“ 合影留 念”体 现出大 家都想 和大熊 猫留住 最美丽 的瞬间 以作纪 念。N othing can be accomplished without norms or standards.
总结反思
小结
知识点 多项式除以单项式的法则
多项式除以单项式，先用这个多项式的每一项除以这 ___单__项_式______，再把所得的____商__相_加___，即(am＋bm am÷m＋bm÷m＋cm÷m＝a＋b＋c. [点拨] 多项式除以单项式的实质就是将多项式除以单 单项式除以单项式的商的和．
12.4 整式的除法
12.4 整式的除法
目标突破
目标一 会用多项式除以单项式的法则进行计算
例 1 [教材例 2 针对训练] 计算： (1)(36x4y3－24x3y2＋18x2y2)÷(－6x2y)； (2)(12m3n4＋16m2n3－8m2n2)÷12mn2.
12.4 整式的除法
解：(1)原式＝36x4y3÷(－6x2y)＋(－24x3y2)÷(－6x2y)＋18x2y2÷(－6 ＋4xy－3y.
解：原式＝(x2－y2－x2＋2xy－y2＋2xy－2y2)÷4y＝(－4y2＋4xy)÷ 当x＝3，y＝1时，原式＝3－1＝2.
12.4 整式的除法
【归纳总结】用多项式除以单项式解决问题时“三注 确解题步骤，做到步步有据； (2)注意商的符号，防止变号错误； (3)注意化简合并，使计算简便．
12.4 整式的除法
(2)(12m3n4＋16m2n3－8m2n2)÷12mn2 ＝(12m3n4＋16m2n3－8m2n2)÷14m2n2 ＝48mn2＋64n－32.
12.4 整式的除法
【归纳总结】应用多项式除以单项式法则的“四注意 (1)基本思想是把多项式除以单项式转化为单项式除以 后把所得的商相加； (2)多项式除以单项式所得的商仍然是多项式，并且商 多项式的项数相同； (3)注意确定商中每一项的符号，“同号得正，异号得 中的每一项都包含它前面的符号； (4)多项式除以单项式与单项式乘以多项式是互逆运算 单项式乘以多项式来验证多项式除以单项式的结果是
第12章 整式的乘除
12. 4 整式的除法 2．多项式除以单项式
第12章 整式的乘除
2. 多项式除以单项
知识目标 目标突破 总结反思
12.4 整式的除法
知识目标
1．经过计算具体的多项式除以单项式，在思考、讨 式除以单项式的运算法则，会用这个法则进行计算． 2．在理解法则的基础上，通过探究、转化，能解决 单项式有关的应用问题． 3．经过对比、思考，掌握与整式除法有关的综合计
12.4 整式的除法
【归纳总结】运用多项式除以单项式解决实际问题的 确列式，再运用法则计算即可．
12.4 整式的除法
目标三 会进行多项式除以单项式的综合计算
例3 [教材补充例题] 先化简，再求值：[(x＋y)·(x－y) 2y(x－y)]÷4y，其中x＝3，y＝1.
【解析】 先按照运算顺序，把括号内较复杂的算式转化为较 式，然后按多项式除以单项式的法则进行计算．