2021年秋七年级数学上册第2章整式的加减集训课堂练素养整式化简求值的常见题型习题课件新人教版

,练素养,课题,2,第二章 整式的加减,集训课堂,整式化简求值的常见题型,1,2,3,4,5,6,7,8,10,11,温馨,提示,：,点击,进入,讲评,9,习题链接,如,图，某长方形广场的四个角都有一块半径相同的四分之一圆形的草地，若圆形的半径为,r,米，长方形的长为,a,米，宽为,b,米,1,(1),分别用整式表示草地和空地的,面积；,(2),若长方形的长为,300,米，宽为,200,米，圆形的半径为,10,米，求广场空地的面积,(,结果精确到个位,),当,a,300,，,b,200,，,r,10,时，,ab,r,2,300200,100,59 686.,故广场空地的面积约为,59 686,平方米,2,解：因为,a,，,b,互为相反数，,c,，,d,互为倒数,，,|,x,|,1,，,所以,a,b,0,，,cd,1,，,x,1,，,当,a,b,0,，,cd,1,，,x,1,时,，原式,0,12,11,0,1,1,0,；当,a,b,0,，,cd,1,，,x,1,时，,原式,0,(,1),2,1(,1),1,(,1),2.,综上所述，式子,a,b,x,2,cdx,的值为,0,或,2.,已知,a,，,b,互为相反数，,c,，,d,互为倒数，,|,x,|,1,，求式子,a,b,x,2,cdx,的值,已知,A,3,a,2,6,ab,b,2,，,B,a,2,5,ab,7,b,2,，,其中,a,1,，,b,1,，求,3,A,2,B,的值,3,解：,3,A,2,B,3(3,a,2,6,ab,b,2,),2(,a,2,5,ab,7,b,2,),9,a,2,18,ab,3,b,2,2,a,2,10,ab,14,b,2,(,9,2),a,2,(18,10),ab,(,3,14),b,2,11,a,2,8,ab,17,b,2,.,当,a,1,，,b,1,时，,11,a,2,8,ab,17,b,2,11(,1)2,8(,1)1,1712,111,8(,1),171,11,(,8),17,36.,所以,3,A,2,B,的值为,36.,解,：由,题意，得,m,1,1,6,，,7,m,3,n,6,，解得,m,4,，,n,1,，所以,m,2,n,2,4,2,1,2,17.,4,(,2),若,a,1,，,b,2,，求该多项式的值,5,已知,A,B,3,x,2,5,x,1,，,A,C,2,x,3,x,2,5,，求当,x,2,时,B,C,的值,提示：,B,C,(,A,B,),(,A,C,),6,解：,B,C,(,A,B,),(,A,C,),3,x,2,5,x,1,(,2,x,3,x,2,5,),3,x,2,5,x,1,2,x,3,x,2,5,(3,3),x,2,(,5,2),x,1,5,3,x,6.,当,x,2,时,，,3,x,6,32,6,6,6,0.,所以当,x,2,时，,B,C,的值为,0.,已知,a,2,a,4,0,，求,4,a,2,2(,a,2,a,3),(,a,2,a,4),4,a,的值,解：原式,4,a,2,2,a,2,2,a,6,a,2,a,4,4,a,a,2,a,2.,又因为,a,2,a,4,0,，所以,a,2,a,4,，,所以,原式,4,2,2.,7,8,已知,(2,x,3),4,a,0,x,4,a,1,x,3,a,2,x,2,a,3,x,a,4,，求下列各式的值；,(1),a,0,a,1,a,2,a,3,a,4,；,解,：将,x,1,代入,(2,x,3),4,a,0,x,4,a,1,x,3,a,2,x,2,a,3,x,a,4,，,得,a,0,a,1,a,2,a,3,a,4,(2,3),4,625.,9,(2),a,0,a,1,a,2,a,3,a,4,；,解：,将,x,1,代入,(2,x,3),4,a,0,x,4,a,1,x,3,a,2,x,2,a,3,x,a,4,，,得,a,0,a,1,a,2,a,3,a,4,(,2,3),4,1.,(3),a,0,a,2,a,4,.,解：,因为,(,a,0,a,1,a,2,a,3,a,4,),(,a,0,a,1,a,2,a,3,a,4,),2(,a,0,a,2,a,4,),，,所以,625,1,2(,a,0,a,2,a,4,),，所以,a,0,a,2,a,4,313.,【,点拨,】,本题中直接求各项系数所组成式子的值是行不通的，观察各式的特点可以发现，通过赋予,x,特殊值可以求出式子的值,解：,(2,x,2,ax,y,6),(2,bx,2,3,x,5,y,1),2,x,2,ax,y,6,2,bx,2,3,x,5,y,1,(2,2,b,),x,2,(,a,3),x,6,y,7.,因为上式的值与字母,x,所取的值无关，,所以,2,2,b,0,，,a,3,0,，即,a,3,，,b,1.,10,已知,三个有理数,a,，,b,，,c,在数轴上的位置如图所示，且,|,a,|,2,，,|,b,|,3,，,|,c,|,1.,求,a,b,c,的值,解：由题意及数轴可知,a,2,，,b,3,，,c,1.,则,a,b,c,2,(,3),1,2,3,1,1,1,2.,所以,a,b,c,的值为,2.,11,