2018年七年级数学上册第二章整式的加减2-2整式的加减2-2-3整式加减的运算法则备课资料教案（新版）新人教版

The Union Jack was the name of the flag made when England,Scotland and Ireland joined together to make one country.

2018年七年级数学上册第二章整式的加减2-2整式的加减2-2-3整式加减的运算法则备课资料教案（新版）新人教版

知识点：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.

关键提醒:整式的加减运算的基础是合并同类项和去括号法则,对这两个知识点要熟练运用.整式的加减与有理数的加减类似,但是整式的加减运算结果不一定是单项式,不是同类项的不能强行合并.

进行整式加减的一般步骤是:(1)如果遇到括号,先按去括号法则,去掉括号;(2)合并同类项. 考点1：列式进行整式的加减

【例1】 已知多项式3x4-5x2-3与另一个多项式的差为2x2-x3-5+3x4,求另一个多项式.

解:设所求多项式为A,则由题意得 (3x4-5x2-3)-A=2x2-x3-5+3x4, 所以A=(3x4-5x2-3)-(2x2-x3-5+3x4) =3x4-5x2-3-2x2+x3+5-3x4 =(3-3)x4+x3+(-5-2)x2+(-3+5) =x3-7x2+2.

Sailors used to speak of a “jack” when they meant a flag which was set near the bow of a sailing ship.The flag showed the coutry to which the ship belonged.The Union Jackbecame the flag of Great Britain.1 / 3

The Union Jack was the name of the flag made when England,Scotland and Ireland joined together to make one country.

点拨：解答此类题目,常设未知整式为A,根据题列出类似于方程的等式,然后求出未知整式.

考点2：利用整体思想求整式的值

【例2】已知a-b=1,则代数式2a-2b-3的值是( ) A.-1 B.1 C.-5 D.5 答案:A

点拨：本题考查整体代入法求代数式的值.逆用分配律可得2a-2b=2(a-b)=2,所以2a-2b-3=2-3=-1. 考点3：逆向思维

【例3】在做某整式减去ab-2bc+3ac时,小芳误以为是加上此式,她得到的答案是2bc-2ac+2ab,请你帮着求出正确的答案.

解:设该整式为A,根据题意得:A+ab-2bc+3ac=2bc-2ac+2ab, 可得A=4bc-5ac+ab.

于是正确的结果为:4bc-5ac+ab-(ab-2bc+3ac)=6bc-8ac. 点拨：要注意根据小芳错误的算法先求出这个整式,然后再按正确的方法计算出正确的结果.

考点4：含有字母的绝对值化简问题

【例4】已知有理数a,b,c对应的点在数轴上的位置如图所示, 试化简|a+c|-|a+b+c|-|b-a|+|b+c|.

解:根据数轴知a+c<0,a+b+c<0,b-a<0,b+c<0,

则|a+c|-|a+b+c|-|b-a|+|b+c| =-(a+c)+(a+b+c)+(b-a)-(b+c)

Sailors used to speak of a “jack” when they meant a flag which was set near the bow of a sailing ship.The flag showed the coutry to which the ship belonged.The Union Jackbecame the flag of Great Britain.2 / 3

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