中考数学复习第一章数与式1.3整式试卷部分市赛课公开课一等奖省名师优质课获奖课件.pptx

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,第一章 数与式,1.3整式,中考数学,(河南专用),1/99,A,组,-,年,河南,中考题组,五年中考,1,.(河南,4,3分)以下运算正确是,(),A.(-,x,2,),3,=-,x,5,B.,x,2,+,x,3,=,x,5,C.,x,3,x,4,=,x,7,D.2,x,3,-,x,3,=1,答案,C选项A,(-,x,2,),3,=-,x,6,错误;选项B,x,2,与,x,3,不是同类项,不能合并,错误;选项C,x,3,x,4,=,x,7,正确;,选项D,2,x,3,-,x,3,=,x,3,错误.故选C.,2/99,2,.(河南,4,3分)以下计算正确是,(),A.,-,=,B.(-3),2,=6,C.3,a,4,-2,a,2,=,a,2,D.(-,a,3,),2,=,a,5,答案,AA项,-,=2,-,=,;B项,(-3),2,=9;C项,3,a,4,与2,a,2,不是同类项,不能合并;D项,(-,a,3,),2,=,a,6,.故选A.,3/99,3,.(河南,4,3分)以下各式计算正确是,(),A.,a,+2,a,=3,a,2,B.(-,a,3,),2,=,a,6,C.,a,3,a,2,=,a,6,D.(,a,+,b,),2,=,a,2,+,b,2,答案,B因为,a,+2,a,=3,a,所以A错;因为(-,a,3,),2,=(-1),2,a,3,2,=,a,6,所以B正确;因为,a,3,a,2,=,a,5,所以C错;因,为(,a,+,b,),2,=,a,2,+2,ab,+,b,2,所以D错,故选B.,4/99,4,.(河南,16,8分)先化简,再求值:,(2,x,+,y,),2,+(,x,-,y,)(,x,+,y,)-5,x,(,x,-,y,),其中,x,=,+1,y,=,-1.,解析,原式=4,x,2,+4,xy,+,y,2,+,x,2,-,y,2,-5,x,2,+5,xy,(3分),=9,xy,.,(5分),当,x,=,+1,y,=,-1时,原式=9,xy,=9,(,+1),(,-1)=9.,(8分),5/99,考点一整式及其运算法则,B,组,-,年全国中考题组,1,.(河北,13,2分)若2,n,+2,n,+2,n,+2,n,=2,则,n,=,(),A.-1B.-2C.0D.,答案,A2,n,+2,n,+2,n,+2,n,=2,4,2,n,=2,2,n,=,n,=-1,故选A.,6/99,2,.(内蒙古包头,5,3分)假如2,x,a,+1,y,与,x,2,y,b,-1,是同类项,那么,值是,(),A.,B.,C.1D.3,答案,A2,x,a,+1,y,与,x,2,y,b,-1,是同类项,解得,=,.故选A.,7/99,3,.(陕西,5,3分)以下计算正确是,(),A.,a,2,a,2,=2,a,4,B.(,a,-2),2,=,a,2,-4,C.(-,a,2,),3,=-,a,6,D.3,a,2,-6,a,2,=3,a,2,答案,C,a,2,a,2,=,a,4,选项A错误;(,a,-2),2,=,a,2,-4,a,+4,选项B错误;(-,a,2,),3,=-,a,6,选项C正确;3,a,2,-6,a,2,=-3,a,2,选,项D错误.故选C.,归纳总结,相关整式计算问题,首先明确所考查运算类型,再依据各自运算法则计算即,可.在运算过程中,一定要注意指数、系数和符号处理,同时还应熟记乘法公式并能灵活运,用.,8/99,4,.(黑龙江哈尔滨,2,3分)以下运算正确是,(),A.,a,6,a,3,=,a,2,B.2,a,3,+3,a,3,=5,a,6,C.(-,a,3,),2,=,a,6,D.(,a,+,b,),2,=,a,2,+,b,2,答案,C,a,6,a,3,=,a,6-3,=,a,3,选项A错误;,2,a,3,+3,a,3,=5,a,3,选项B错误;,(-,a,3,),2,=,a,6,选项C正确;,(,a,+,b,),2,=,a,2,+2,ab,+,b,2,选项D错误,故选C.,9/99,5,.(湖北武汉,3,3分)以下计算中正确是,(),A.,a,a,2,=,a,2,B.2,a,a,=2,a,2,C.(2,a,2,),2,=2,a,4,D.6,a,8,(3,a,2,)=2,a,4,答案,BA项:,a,a,2,=,a,1+2,=,a,3,错误;B项:2,a,a,=2,a,1+1,=2,a,2,正确;C项:(2,a,2,),2,=4,a,2,2,=4,a,4,错误;D项:6,a,8,(3,a,2,)=2,a,8-2,=2,a,6,错误.故选B.,10/99,6,.(内蒙古呼和浩特,5,3分)以下运算正确是,(),A.,a,2,+,a,3,=,a,5,B.(-2,a,2,),3,=-16,a,4,C.3,a,-1,=,D.(2,a,2,-,a,),2,3,a,2,=4,a,2,-4,a,+1,答案,D因为,a,2,与,a,3,不是同类项,不能合并,所以选项A错;因为(-2,a,2,),3,=-8,a,6,=-32,a,4,所,以选项B错;因为3,a,-1,=,所以选项C错.故选D.,11/99,7,.(天津,13,3分)计算,x,7,x,4,结果等于,.,答案,x,3,解析,依据同底数幂除法法则可得,原式=,x,7-4,=,x,3,.,12/99,8,.(辽宁沈阳,14,3分)三个连续整数中,n,是最大一个,这三个数和为,.(用含,n,代,数式表示),答案,3,n,-3,解析,三个连续整数中,n,是最大一个,则前两个分别为,n,-1,n,-2,所以这三个数和为,n,+(,n,-1)+,(,n,-2)=3,n,-3.,13/99,9,.(河北,21,10分)老师在黑板上书写了一个正确演算过程,随即用手掌捂住了一个二次,三项式,形式以下:,-3,x,=,x,2,-5,x,+1.,(1)求所捂二次三项式;,(2)若,x,=,+1,求所捂二次三项式值.,解析,(1)设所捂二次三项式为,A,则,A,=,x,2,-5,x,+1+3,x,(2分),=,x,2,-2,x,+1.,(4分),(2)若,x,=,+1,则,A,=(,x,-1),2,(6分),=(,+1-1),2,(7分),=6.,(10分),14/99,1,.(河北,4,3分)将9.5,2,变形正确是,(),A.9.5,2,=9,2,+0.5,2,B.9.5,2,=(10+0.5),(10-0.5),C.9.5,2,=10,2,-2,10,0.5+0.5,2,D.9.5,2,=9,2,+9,0.5+0.5,2,考点二乘法公式,答案,C9.5,2,=(10-0.5),2,=10,2,-2,10,0.5+0.5,2,故选C.,15/99,2,.(湖北武汉,5,3分)利用乘法公式计算(,x,+3),2,结果是,(),A.,x,2,+9B.,x,2,-6,x,+9C.,x,2,+6,x,+9D.,x,2,+3,x,+9,答案,C依据乘法公式得(,x,+3),2,=,x,2,+6,x,+9.故选C.,16/99,3,.(四川南充,14,3分)假如,x,2,+,mx,+1=(,x,+,n,),2,且,m,0,则,n,值是,.,答案,1,解析,因为(,x,+,n,),2,=,x,2,+2,nx,+,n,2,=,x,2,+,mx,+1,所以,所以,m,0,n,0,n,=1.,17/99,4,.(江西,13(1),3分)计算:(,a,+1)(,a,-1)-(,a,-2),2,.,解析,原式=,a,2,-1-(,a,2,-4,a,+4)=4,a,-5.,18/99,5,.(吉林,15,5分)先化简,再求值:(,x,+2)(,x,-2)+,x,(4-,x,),其中,x,=,.,解析,原式=,x,2,-4+4,x,-,x,2,(2分),=4,x,-4.,(3分),当,x,=,时,原式=4,-4=-3.,(5分),19/99,6,.(吉林长春,15,6分)先化简,再求值:(,x,+1),2,+,x,(,x,-2),其中,x,=,.,解析,原式=,x,2,+2,x,+1+,x,2,-2,x,=2,x,2,+1.,(4分),当,x,=,时,原式=2,(,),2,+1=7.,(6分),20/99,1,.(安徽,5,4分)以下分解因式正确是,(),A.-,x,2,+4,x,=-,x,(,x,+4)B.,x,2,+,xy,+,x,=,x,(,x,+,y,),C.,x,(,x,-,y,)+,y,(,y,-,x,)=(,x,-,y,),2,D.,x,2,-4,x,+4=(,x,+2)(,x,-2),考点三因式分解,答案,C对于A,结果应是-,x,(,x,-4);对于B,结果应是,x,(,x,+,y,+1);对于D,结果应是(,x,-2),2,故选C.,21/99,2,.(山东临沂,9,3分)多项式,mx,2,-,m,与多项式,x,2,-2,x,+1公因式是,(),A.,x,-1B.,x,+1C.,x,2,-1D.(,x,-1),2,答案,A,mx,2,-,m,=,m,(,x,2,-1)=,m,(,x,+1)(,x,-1),x,2,-2,x,+1=(,x,-1),2,公因式为,x,-1.故选A.,22/99,3,.(湖北黄冈,8,3分)因式分解:,x,3,-9,x,=,.,答案,x,(,x,+3)(,x,-3),解析,x,3,-9,x,=,x,(,x,2,-9)=,x,(,x,+3)(,x,-3).,23/99,4.,(吉林,9,3分)分解因式:,a,2,+4,a,+4=,.,答案,(,a,+2),2,解析,由完全平方公式,可得,a,2,+4,a,+4=(,a,+2),2,.,24/99,5,.(安徽,12,5分)因式分解:,a,2,b,-4,ab,+4,b,=,.,答案,b,(,a,-2),2,解析,a,2,b,-4,ab,+4,b,=,b,(,a,2,-4,a,+4)=,b,(,a,-2),2,.,25/99,6,.(江苏南京,9,2分)分解因式2,a,(,b,+,c,)-3(,b,+,c,)结果是,.,答案,(,b,+,c,)(2,a,-3),解析,2,a,(,b,+,c,)-3(,b,+,c,)=(,b,+,c,)(2,a,-3).,26/99,7,.(黑龙江哈尔滨,14,3分)把多项式,ax,2,+2,a,2,x,+,a,3,分解因式结果是,.,答案,a,(,x,+,a,),2,解析,原式=,a,(,x,2,+2,ax,+,a,2,)=,a,(,x,+,a,),2,.,27/99,8,.(北京,11,3分)分解因式:5,x,3,-10,x,2,+5,x,=,.,答案,5,x,(,x,-1),2,解析,5,x,3,-10,x,2,+5,x,=5,x,(,x,2,-2,x,+1)=5,x,(,x,-1),2,.,28/99,考点一整式及其运算法则,C,组,教师专用题组,1,.(安徽,3,4分)以下运算正确是,(),A.(,a,2,),3,=,a,5,B.,a,4,a,2,=,a,8,C.,a,6,a,3,=,a,2,D.(,ab,),3,=,a,3,b,3,答案,D对于A,结果应是,a,6,故A错;对于B,结果应是,a,6,故B错;对于C,结果应是,a,3,故C错,所以,选D.,29/99,2,.(四川成都,5,3分)以下计算正确是,(),A.,x,2,+,x,2,=,x,4,B.(,x,-,y,),2,=,x,2,-,y,2,C.(,x,2,y,),3,=,x,6,y,D.(-,x,),2,x,3,=,x,5,答案,D选项A,x,2,+,x,2,=2,x,2,错误;选项B,(,x,-,y,),2,=,x,2,-2,xy,+,y,2,错误;选项C,(,x,2,y,),3,=,x,6,y,3,错误;选项D,(-,x,),2,x,3,=,x,2,x,3,=,x,5,正确.故选D.,30/99,3,.(辽宁沈阳,5,2分)以下运算错误是,(),A.(,m,2,),3,=,m,6,B.,a,10,a,9,=,a,C.,x,3,x,5,=,x,8,D.,a,4,+,a,3,=,a,7,答案,D选项A,幂乘方,底数不变,指数相乘;选项B,同底数幂相除,底数不变,指数相减;选,项C,同底数幂相乘,底数不变,指数相加;选项D,不是同类项不能合并.故D错误.,方法总结,这类考题,扎实掌握整式运算法则和运算律是关键.,31/99,4,.(湖北武汉,5,3分)计算(,a,-2)(,a,+3)结果是,(),A.,a,2,-6B.,a,2,+,a,-6,C.,a,2,+6D.,a,2,-,a,+6,答案,B(,a,-2)(,a,+3)=,a,2,+3,a,-2,a,-6=,a,2,+,a,-6,故选B.,32/99,5,.(新疆乌鲁木齐,3,4分)以下运算正确是,(),A.,x,3,+,x,3,=2,x,6,B.,x,2,x,3,=,x,6,C.,x,3,x,=,x,3,D.(-2,x,2,),3,=-8,x,6,答案,D对于A,结果应是2,x,3,故A错;对于B,结果应是,x,5,故B错;对于C,结果应是,x,2,故C错,所以,选D.,33/99,6,.(福建,4,4分)化简(2,x,),2,结果是,(),A.,x,4,B.2,x,2,C.4,x,2,D.4,x,答案,C依据积乘方法则可知,(2,x,),2,=2,2,x,2,=4,x,2,故选C.,34/99,7,.(江西,4,3分)以下运算正确是,(),A.(-,a,5,),2,=,a,10,B.2,a,3,a,2,=6,a,2,C.-2,a,+,a,=-3,a,D.-6,a,6,2,a,2,=-3,a,3,答案,A2,a,3,a,2,=6,a,3,故B错误;-2,a,+,a,=-,a,故C错误;-6,a,6,2,a,2,=-3,a,4,故D错误.故选A.,35/99,8,.(内蒙古呼和浩特,8,3分)以下运算正确是,(),A.(,a,2,+2,b,2,)-2(-,a,2,+,b,2,)=3,a,2,+,b,2,B.,-,a,-1=,C.(-,a,),3,m,a,m,=(-1),m,a,2,m,D.6,x,2,-5,x,-1=(2,x,-1)(3,x,-1),答案,C(,a,2,+2,b,2,)-2(-,a,2,+,b,2,)=,a,2,+2,b,2,+2,a,2,-2,b,2,=3,a,2,故A错误;,-,a,-1=,=,故B错误;,6,x,2,-5,x,+1=(2,x,-1)(3,x,-1),故D错误,故选C.,36/99,9,.(湖北武汉,5,3分)计算(,x,+1)(,x,+2)结果为,(),A.,x,2,+2B.,x,2,+3,x,+2,C.,x,2,+3,x,+3D.,x,2,+2,x,+2,答案,B(,x,+1)(,x,+2)=,x,2,+2,x,+,x,+2=,x,2,+3,x,+2.故选B.,37/99,10,.(山西,5,3分)以下运算,是,(),A.(,-1),0,=1B.(-3),2,=,C.5,x,2,-6,x,2,=-,x,2,D.(2,m,3,),2,(2,m,),2,=,m,4,答案,B任何非零数零次幂都是1,A正确;(-3),2,=9,=4,B错误;5,x,2,-6,x,2,=(5-6),x,2,=-,x,2,C正确;(2,m,3,),2,(2,m,),2,=2,2,(,m,3,),2,(2,2,m,2,)=4,m,6,(4,m,2,)=(4,4)(,m,6,m,2,)=,m,4,D正确.,38/99,11,.(广西南宁,7,3分)以下运算正确是,(),A.,a,2,-,a,=,a,B.,ax,+,ay,=,axy,C.,m,2,m,4,=,m,6,D.(,y,3,),2,=,y,5,答案,C选项A中,a,2,与,a,不是同类项,不能合并;选项B结果应是,a,(,x,+,y,);选项D结果应是,y,6,.,故选C.,39/99,12,.(黑龙江哈尔滨,2,3分)以下运算正确是,(),A.,a,2,a,3,=,a,6,B.(,a,2,),3,=,a,5,C.(-2,a,2,b,),3,=-8,a,6,b,3,D.(2,a,+1),2,=4,a,2,+2,a,+1,答案,C,a,2,a,3,=,a,2+3,=,a,5,故选项A错误;(,a,2,),3,=,a,2,3,=,a,6,故选项B错误;(2,a,+1),2,=4,a,2,+4,a,+1,故选项D错,误.故选C.,40/99,13,.(辽宁沈阳,6,2分)以下计算正确是,(),A.,x,4,+,x,4,=2,x,8,B.,x,3,x,2,=,x,6,C.(,x,2,y,),3,=,x,6,y,3,D.(,x,-,y,)(,y,-,x,)=,x,2,-,y,2,答案,CA项:,x,4,+,x,4,=2,x,4,本选项错误;,B项:,x,3,x,2,=,x,3+2,=,x,5,本选项错误;,C项:(,x,2,y,),3,=(,x,2,),3,y,3,=,x,6,y,3,本选项正确;,D项:(,x,-,y,)(,y,-,x,)=-(,x,-,y,),2,本选项错误.故选C.,41/99,14,.(山东青岛,4,3分)计算,a,a,5,-(2,a,3,),2,结果为,(),A.,a,6,-2,a,5,B.-,a,6,C.,a,6,-4,a,5,D.-3,a,6,答案,D,a,a,5,-(2,a,3,),2,=,a,6,-4,a,6,=-3,a,6,故选D.,42/99,15,.(吉林,4,2分)计算(-,a,3,),2,结果正确是,(),A.,a,5,B.-,a,5,C.-,a,6,D.,a,6,答案,D(-,a,3,),2,=(-1),2,(,a,3,),2,=,a,6,故选D.,43/99,16,.(河北,2,3分)计算正确是,(),A.(-5),0,=0B.,x,2,+,x,3,=,x,5,C.(,ab,2,),3,=,a,2,b,5,D.2,a,2,a,-1,=2,a,答案,D选项A中,(-5),0,=1;选项B中,x,2,与,x,3,不是同类项,不能合并;选项C中,(,ab,2,),3,=,a,3,b,6,.故选D.,44/99,17,.(江苏南京,3,2分)以下计算中,结果是,a,6,是,(),A.,a,2,+,a,4,B.,a,2,a,3,C.,a,12,a,2,D.(,a,2,),3,答案,D,a,2,与,a,4,不是同类项,不能合并,选项A不符合;,a,2,a,3,=,a,2+3,=,a,5,选项B不符合;,a,12,a,2,=,a,12-2,=,a,10,选项C不符合;(,a,2,),3,=,a,2,3,=,a,6,故选D.,45/99,18,.(安徽,2,4分)计算,a,10,a,2,(,a,0)结果是,(),A.,a,5,B.,a,-5,C.,a,8,D.,a,-8,答案,C,a,10,a,2,=,a,10-2,=,a,8,故选C.,46/99,19,.(辽宁沈阳,5,3分)以下计算结果正确是,(),A.,a,4,a,2,=,a,8,B.(,a,5,),2,=,a,7,C.(,a,-,b,),2,=,a,2,-,b,2,D.(,ab,),2,=,a,2,b,2,答案,DA项,依据同底数幂乘法法则得,a,4,a,2,=,a,4+2,=,a,6,故本选项错误;B项,依据幂乘方法,则得(,a,5,),2,=,a,5,2,=,a,10,故本选项错误;C项,依据完全平方公式得(,a,-,b,),2,=,a,2,-2,ab,+,b,2,故本选项错误;D项,依据积乘方法则得(,ab,),2,=,a,2,b,2,故本选项正确.故选D.,47/99,20,.(内蒙古呼和浩特,6,3分)以下运算,结果正确是,(),A.,m,2,+,m,2,=,m,4,B.,=,m,2,+,C.(3,mn,2,),2,=6,m,2,n,4,D.2,m,2,n,=2,mn,2,答案,D2,m,2,n,=2,m,2,n,=2,mn,2,故选D.,48/99,21,.(浙江宁波,2,4分)以下计算正确是,(),A.(,a,2,),3,=,a,5,B.2,a,-,a,=2,C.(2,a,),2,=4,a,D.,a,a,3,=,a,4,答案,DA.(,a,2,),3,=,a,2,3,=,a,6,a,5,A选项错误;,B.2,a,-,a,=(2-1),a,=,a,2,B选项错误;,C.(2,a,),2,=2,2,a,2,=4,a,2,4,a,C选项错误;,D.,a,a,3,=,a,1+3,=,a,4,D选项正确.,故选D.,49/99,22,.(山东威海,7,3分)以下运算正确是,(),A.(-3,mn,),2,=-6,m,2,n,2,B.4,x,4,+2,x,4,+,x,4,=6,x,4,C.(,xy,),2,(-,xy,)=-,xy,D.(,a,-,b,)(-,a,-,b,)=,a,2,-,b,2,答案,C(-3,mn,),2,=9,m,2,n,2,4,x,4,+2,x,4,+,x,4,=7,x,4,(,xy,),2,(-,xy,)=-(,xy,),2,(,xy,)=-,xy,(,a,-,b,)(-,a,-,b,)=-(,a,-,b,)(,a,+,b,)=-,a,2,+,b,2,只有选项C正确.故选C.,50/99,23,.(浙江绍兴,4,4分)下面是一位同学做四道题:2,a,+3,b,=5,ab,.(3,a,3,),2,=6,a,6,.,a,6,a,2,=,a,3,.,a,2,a,3,=,a,5,.其中做正确一道题序号是,(),A.B.C.D.,答案,D,a,2,a,3,=,a,2+3,=,a,5,故选D.,51/99,24,.(上海,7,4分)计算:2,a,a,2,=,.,答案,2,a,3,解析,2,a,a,2,=2,a,1+2,=2,a,3,.,52/99,25,.(北京,12,3分)下列图中四边形均为矩形.依据图形,写出一个正确等式:,.,答案,答案不唯一.如:,m,(,a,+,b,+,c,)=,ma,+,mb,+,mc,解析,如图,S,矩形,ABEF,=,m,(,a,+,b,+,c,),S,矩形,ABCH,=,ma,S,矩形,HCDG,=,mb,S,矩形,GDEF,=,mc,S,矩形,ABEF,=,S,矩形,ABCH,+,S,矩形,HCDG,+,S,矩,形,GDEF,m,(,a,+,b,+,c,)=,ma,+,mb,+,mc,.,53/99,26,.(四川绵阳,13,3分)计算:,a,(,a,2,a,)-,a,2,=,.,答案,0,解析,原式=,a,a,-,a,2,=,a,2,-,a,2,=0.,54/99,27,.(安徽,14,5分)已知实数,a,、,b,、,c,满足,a,+,b,=,ab,=,c,有以下结论:,若,c,0,则,+,=1;,若,a,=3,则,b,+,c,=9;,若,a,=,b,=,c,则,abc,=0;,若,a,、,b,、,c,中只有两个数相等,则,a,+,b,+,c,=8.,其中正确是,.(把全部正确结论序号都选上),解析,c,0,a,+,b,=,ab,0.等式两边同时除以,ab,得,+,=1,正确;当,a,=3时,解方程3+,b,=3,b,=,c,可得,b,=,c,=,b,+,c,=6,故错误;,a,=,b,=,c,则2,a,=,a,2,=,a,a,=0,abc,=0,故正确;,a,、,b,、,c,中只有两个数相等,a,=,b,(若,a,=,c,则由,a,+,b,=,ab,=,c,得,a,=,b,=,c,=0,不合题意,故,a,c,同理,b,c,),则2,a,=,a,2,a,=0或,a,=2.,a,=0不合题意,a,=2,则,b,=2,c,=4,a,+,b,+,c,=8,故正确.,答案,55/99,28,.(内蒙古呼和浩特,15,3分)若实数,a,、,b,满足(4,a,+4,b,)(4,a,+4,b,-2)-8=0,则,a,+,b,=,.,答案,-,或1,解析,由(4,a,+4,b,)(4,a,+4,b,-2)-8=0得(,a,+,b,)(2,a,+2,b,-1)-1=0,则2(,a,+,b,),2,-(,a,+,b,)-1=0,解得,a,+,b,=-,或1.,评析,在本题中,需要把,a,+,b,看成一个整体,结构一元二次方程,解得(,a,+,b,)值.属于轻易题.,56/99,29,.(河北,20,8分)嘉淇准备完成题目:,发觉系数“,”印刷不清楚.,(1)他把“,”猜成3,请你化简:(3,x,2,+6,x,+8)-(6,x,+5,x,2,+2);,(2)他妈妈说:“你猜错了,我看到该题标准答案结果是常数.”经过计算说明原题中“,”是,几.,解析,(1)原式=3,x,2,+6,x,+8-6,x,-5,x,2,-2,=-2,x,2,+6.,(2)设“,”为,a,则原式=,ax,2,+6,x,+8-6,x,-5,x,2,-2,=(,a,-5),x,2,+6.,结果是常数,a,=5.,思绪分析,(1)去括号、合并同类项即可得出结论;,(2)设“,”是,a,将,a,看作常数,去括号、合并同类项后得到(,a,-5),x,2,+6,依据结果为常数可知二次,项系数为0,进而得出,a,值.,57/99,1,.(云南,14,4分)已知,x,+,=6,则,x,2,+,=,(),A.38B.36C.34D.32,考点二乘法公式,答案,C,x,+,=6,=,x,2,+,+2=36,x,2,+,=34.,思绪分析,由,x,+,值求,x,2,+,值,考虑整体代入法,将,x,+,平方后转化为含,x,2,+,形式,进,而求解.,方法总结,灵活应用完全平方公式是处理本题关键.,58/99,2,.(宁夏,2,3分)以下计算正确是,(),A.,+,=,B.(-,a,2,),2,=-,a,4,C.(,a,-2),2,=,a,2,-4D.,=,(,a,0,b,0),答案,D因为,与,不能合并,所以选项A错;因为(-,a,2,),2,=,a,4,所以选项B错;因为(,a,-2),2,=,a,2,-4,a,+,4,所以选项C错;易知D正确,故选D.,59/99,3,.(贵州遵义,5,3分)以下运算正确是,(),A.4,a,-,a,=3B.2(2,a,-,b,)=4,a,-,b,C.(,a,+,b,),2,=,a,2,+,b,2,D.(,a,+2)(,a,-2)=,a,2,-4,答案,D因为4,a,-,a,=3,a,2(2,a,-,b,)=4,a,-2,b,(,a,+,b,),2,=,a,2,+2,ab,+,b,2,(,a,+2)(,a,-2)=,a,2,-4,所以选项A、B、C错,误,D正确,故选D.,60/99,4,.(湖北黄冈,10,3分)若,a,-,=,则,a,2,+,值为,.,答案,8,解析,因为,a,-,=,所以,=,a,2,+,-2=6,所以,a,2,+,=6+2=8.,61/99,5,.(河北,18,3分)若,a,b,互为相反数,则,a,2,-,b,2,=,.,答案,0,解析,a,b,互为相反数,a,+,b,=0,则,a,2,-,b,2,=(,a,+,b,)(,a,-,b,)=0.,62/99,6.,(天津,14,3分)计算(,+,)(,-,)结果等于,.,答案,3,解析,原式=(,),2,-(,),2,=6-3=3.,63/99,7,.(吉林,9,3分)若,x,2,-4,x,+5=(,x,-2),2,+,m,则,m,=,.,答案,1,解析,x,2,-4,x,+5=,x,2,-4,x,+4-4+5=(,x,-2),2,+1,所以,m,=1.,评析,本题是恒等式问题,也能够先把等号右侧化简得,x,2,-4,x,+4+,m,观察等号两边式子,能够,知道4+,m,=5,可得,m,=1.本题考查了配方法,属轻易题.,64/99,8,.(重庆,21(1),5分)计算:(,a,+,b,),2,-,b,(2,a,+,b,).,解析,原式=,a,2,+2,ab,+,b,2,-2,ab,-,b,2,(3分),=,a,2,.,(5分),9,.(福建龙岩,18,6分)先化简,再求值:(,x,+1)(,x,-1)+,x,(2-,x,)+(,x,-1),2,其中,x,=2,.,解析,原式=,x,2,-1+2,x,-,x,2,+,x,2,-2,x,+1=,x,2,.,(4分),当,x,=2,时,原式=(2,),2,=12.,(6分),65/99,10,.(江西南昌,15,6分)先化简,再求值:2,a,(,a,+2,b,)-(,a,+2,b,),2,其中,a,=-1,b,=,.,解析,解法一:原式=2,a,2,+4,ab,-(,a,2,+4,ab,+4,b,2,),=2,a,2,+4,ab,-,a,2,-4,ab,-4,b,2,=,a,2,-4,b,2,.,(4分),当,a,=-1,b,=,时,原式=(-1),2,-4,(,),2,=-11.,(6分),解法二:原式=(,a,+2,b,)(2,a,-,a,-2,b,),=(,a,+2,b,)(,a,-2,b,)=,a,2,-4,b,2,.,(4分),当,a,=-1,b,=,时,原式=(-1),2,-4,(,),2,=-11.,(6分),66/99,11,.(福建福州,16,7分)先化简,再求值:(,x,+2),2,+,x,(2-,x,),其中,x,=,.,解析,原式=,x,2,+4,x,+4+2,x,-,x,2,=6,x,+4.,当,x,=,时,原式=6,+4=6.,67/99,1,.(云南,4,3分)分解因式:,x,2,-4=,.,考点三因式分解,答案,(,x,-2)(,x,+2),解析,利用平方差公式进行因式分解,x,2,-4=(,x,-2)(,x,+2).,68/99,2.,(内蒙古呼和浩特,11,3分)分解因式,a,2,b,-9,b,=,.,答案,b,(,a,+3)(,a,-3),解析,a,2,b,-9,b,=,b,(,a,2,-9)=,b,(,a,+3)(,a,-3).,69/99,3,.(四川绵阳,13,3分)因式分解:8,a,2,-2=,.,答案,2(2,a,+1)(2,a,-1),解析,8,a,2,-2=2(4,a,2,-1)=2(2,a,),2,-1,2,=2(2,a,+1)(2,a,-1).,70/99,4,.(广东,12,4分)分解因式:,m,2,-4=,.,答案,(,m,+2)(,m,-2),解析,m,2,-4=,m,2,-2,2,=(,m,+2)(,m,-2).,评析,本题考查因式分解、平方差公式.,71/99,5,.(吉林,8,3分)分解因式:3,x,2,-,x,=,.,答案,x,(3,x,-1),解析,3,x,2,-,x,=,x,(3,x,-1).,72/99,6,.(安徽,12,5分)因式分解:,a,3,-,a,=,.,答案,a,(,a,+1)(,a,-1),解析,a,3,-,a,=,a,(,a,2,-1)=,a,(,a,+1)(,a,-1).,评析,本题考查了因式分解,属轻易题.,73/99,7,.(宁夏,9,3分)分解因式:,mn,2,-,m,=,.,答案,m,(,n,+1)(,n,-1),解析,原式=,m,(,n,2,-1)=,m,(,n,+1)(,n,-1).,74/99,8,.(内蒙古呼和浩特,12,3分)分解因式:,x,3,-,x,=,.,答案,x,(,x,+1)(,x,-1),解析,x,3,-,x,=,x,(,x,2,-1)=,x,(,x,+1)(,x,-1).,75/99,9,.(浙江杭州,12,4分)分解因式:,m,3,n,-4,mn,=,.,答案,mn,(,m,+2)(,m,-2),解析,m,3,n,-4,mn,=,mn,(,m,2,-4)=,mn,(,m,+2)(,m,-2).,76/99,10,.(黑龙江哈尔滨,14,3分)把多项式9,a,3,-,ab,2,分解因式结果是,.,答案,a,(3,a,+,b,)(3,a,-,b,),解析,原式=,a,(9,a,2,-,b,2,)=,a,(3,a,),2,-,b,2,=,a,(3,a,+,b,)(3,a,-,b,).,77/99,11,.(四川绵阳,15,3分)在实数范围内因式分解:,x,2,y,-3,y,=,.,答案,y,(,x,-,)(,x,+,),解析,原式=,y,(,x,2,-3)=,y,(,x,-,)(,x,+,).,78/99,12,.(山东威海,15,3分)因式分解:-2,x,2,y,+12,xy,-18,y,=,.,答案,-2,y,(,x,-3),2,解析,-2,x,2,y,+12,xy,-18,y,=-2,y,(,x,2,-6,x,+9),=-2,y,(,x,-3),2,.,79/99,13,.(湖北黄冈,10,3分)分解因式:(2,a,+1),2,-,a,2,=,.,答案,(3,a,+1)(,a,+1),解析,(2,a,+1),2,-,a,2,=(2,a,+1+,a,)(2,a,+1-,a,),=(3,a,+1)(,a,+1).,80/99,14,.(山西,16(2),5分)分解因式:(,y,+2,x,),2,-(,x,+2,y,),2,.,解析,解法一:(,y,+2,x,),2,-(,x,+2,y,),2,=(,y,+2,x,)+(,x,+2,y,)(,y,+2,x,)-(,x,+2,y,),(2分),=(,y,+2,x,+,x,+2,y,)(,y,+2,x,-,x,-2,y,),(3分),=(3,x,+3,y,)(,x,-,y,),(4分),=3(,x,+,y,)(,x,-,y,).,(5分),解法二:(,y,+2,x,),2,-(,x,+2,y,),2,=,y,2,+4,xy,+4,x,2,-(,x,2,+4,xy,+4,y,2,),(1分),=,y,2,+4,xy,+4,x,2,-,x,2,-4,xy,-4,y,2,(2分),=3,x,2,-3,y,2,(3分),=3(,x,2,-,y,2,),(4分),=3(,x,-,y,)(,x,+,y,).,(5分),方法规律,因式分解普通步骤:“一提”“二套”“三分组”“四检验”,先考虑经过提公,因式,套用公式法处理,不行再考虑用分组分解法求解,最终检验因式分解是否彻底正确.,81/99,考点一整式及其运算法则,1,.(许昌一模,5)以下运算正确是,(),A.,a,6,a,3,=,a,2,B.3,a,2,2,a,=6,a,3,C.(3,a,),2,=3,a,2,D.2,x,2,-,x,2,=1,三年模拟,A,组,年模拟基础题组,答案,B选项A,a,6,a,3,=,a,3,故错误;选项B,3,a,2,2,a,=6,a,3,故正确;选项C,(3,a,),2,=9,a,2,故错误;选项D,2,x,2,-,x,2,=,x,2,故错误.故选B.,82/99,2,.(濮阳一模,4)以下计算正确是,(),A.(,a,2,),3,=,a,6,B.,a,2,+,a,2,=,a,4,C.(3,a,)(2,a,)=6,a,D.3,a,-,a,=3,答案,A(,a,2,),3,=,a,2,3,=,a,6,选项A正确;,a,2,+,a,2,=2,a,2,选项B错;(3,a,)(2,a,)=(2,3),a,2,=6,a,2,选,项C错;3,a,-,a,=2,a,选项D错.故选A.,83/99,3,.(开封一模,4)以下计算正确是,(),A.(,a,-2),2,=,a,2,-4B.,a,2,a,4,=,a,8,C.,a,3,+,a,2,=2,a,5,D.(-,ab,2,),3,=-,a,3,b,6,答案,D因为(,a,-2),2,=,a,2,-4,a,+4,a,2,a,4,=,a,6,(,a,3,+,a,2,)不能合并,(-,ab,2,),3,=-,a,3,b,2,3,=-,a,3,b,6,所以选项D正确,故,选D.,84/99,4.,(开封一模,5)以下运算正