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教育头条 > 初中数学 > 初一数学重点难点总结整式的加减知识点总结

初一数学重点难点总结整式的加减知识点总结

初中数学 09-20 浏览量: 分享:

  初一数学重点难点总结整式的加减知识点总结。新初一已经慢慢适应中学的学习生活了吧,今天三好网初中数学辅导老师整理出初一数学,整式的加减知识点总结,帮助大家回顾温习。


 

  初一数学整式的加减知识点整式的加减


  12.1整式


  ①在含有字母的式子中如果出现乘号,通常将乘号写作“·”或省略不写。例如,100×t可以写成100·t或100t。


  ②我们来看几个式子:


  100t,0.8p,mn,a2h,-n,


  这些式子有什么特点呢?


  这些式子都是数或字母的积,像这样的式子叫做单项式(monomial)。


  ③解释一下:


  ⑴单项式中的数字因数叫做这个单项式的系数(coefficient)。例如,单项式100t,a2h,-n的系数分别是100,1,-1。单项式表示数与字母相乘时,通常把数写在前面。


  ⑵一个单项式中,所有字母的指数的和叫做这个单项式的次数(degree  of  a  monomial)。例如,在单项式100t中,字母t的指数是1,100t的次数是1;在单项式a2h中,字母a与h的指数的和是3,a2h的次数是3.


  温馨提示:对于单独一个非常的数,规定它的次数为0.


  ④举个栗子:


  x2+2x+18


  ⑴像这样,几个单项式的和叫做多项式(polynomial)。其中每个单项式叫做多项式的项(term),不含字母的项叫做常数项(constant  term)。例如,多项式u-2.5的项是u与-2.5,其中-2.5是常数项;多项式x2,2x与18,其中18是常数项。


  ⑵多项式里,次数最高项的次数,叫做这个多项式的次数(degree  of  a  polynomial)。例如,多项式u-2.5中次数最高项是一次项u,这个多项式的次数是1;多项式x2+2x+18中次数最高项是二次项x2,这个多项式的次数是2。


  ⑤单项式与多项式统称为整式(integral  expression)。例如,上面见到的单项式100t,0.8p,mn,a2h,-n,以及多项式u+2.5,u-2.5,3x+5y+2z,ab-πr2,x2+2x+18等都是等式。


  考考你:


  u+2.5,3x+5y+2z,ab-πr2的项分别是什么?次数分别是什么?


  解(自己试着做一做):


  22.2整式的加减


  ①像100t与-252t,3x2与2x2,3ab2与-4ab2这样,所含字母相同,并且相同字母的指数也相同的项叫做同类项。几个常数项也是同类项。


  ②把多项式中的同类项合并成一项,叫做合并同类项。


  合并同类项后,所得项的系数是合并前各同类项的系数的和,且字母连同它的指数不变。


  温馨提示:


  注意分配律的使用哦!


  温馨提示:通常我们把一个多项式的各项按照某个字母的指数从大到小(降幂)或者从小到大(升幂)的顺序排列,如-4x2+5x+5也可以写成5+5x-4x2。


  ③去括号时符号变化的规律:


  ⑴如果括号外的因数是正数,去括号后原括号内各项的符号与原来的符号相同;


  ⑵如果括号外的因数是负数,去括号后原括号内各项的符号与原来的符号相反。


  特别地,+(x-3)与-(x-3)可以分别看作1与-1分别乘(x-3)。


  利用分配律,可以将式子中的括号去掉,得


  +(x-3)=x-3,


  -(x-3)=-x+3.


  这也符合以上发现的去括号规律。


  我们可以利用上面的去括号规律进行整式化简。


  小知识:


  顺水航速=船速+水速


  逆水航速=船速-水速


  ④整式加减的运算法则:


  一般地,几个整式相加减,如果有括号就先去括号,然后再合并同类项。


  温馨提示:如遇x-2(x-y2)+(-x+y2),其中x=  -2,y=。像这样求这个算式的值,可以先将式子化简,再代入数值进行计算比较简便。

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