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1、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,2024/9/13 Friday,#,北师大版七年级数学上册课件,第三章第,2,节,整式的加减,第,2,课,时,课时目标,素养达成,1,.,归纳去括号法则,能利用法则进行去括号运算,模型观念、运算能力、抽象能力,2,.,会进行整式的加减运算,并能说明其中的算理,能有条理地思考及提高语言表达能力,模型观念、运算能力、应用意识,【课前预习】,【要点归纳】,【对点小练】,1,.,下列式子中,去括号错误的,是,(),A,.,5,x,-,(,x,-2,y,)=5,x,-,x,+2,y,B,.,2,a,+(-3,a,-,b
2、,)=2,a,-3,a,-,b,C,.,-(,x,+6)=-,x,+6,D,.,-(,x,2,+,y,2,)=-,x,2,-,y,2,2,.,将代数式,-2(,x,-3,y,+1),去括号后,得到的正确结果,是,(),A,.,-2,x,+3,y,-1B,.,-2,x,-6,y,+2,C,.,-2,x,+6,y,-2D,.,-2,x,+5,y,-2,3,.,化简,:(4,a,-2)-3(-1+,a,)=,_,.,C,C,a,+1,【典例微课,】,【重点,1,】,去括号化简,(,模型观念、运算能力、抽象能力,),【典例,1,】,(,教材再开发,P90,例,3,拓展,),先去括号,再合并同类项,.,
3、(1)3,a,-(4,b,-2,a,+1);,(2)2(5,a,-3,b,)-3(,a,2,-2,b,),.,【自主解答】,(1),原式,=3,a,-4,b,+2,a,-1=5,a,-4,b,-1;,(2),原式,=10,a,-6,b,-3,a,2,+6,b,=10,a,-3,a,2,.,【变式训练】,1,.,(2024,岳阳期中,),下列去括号正确的,是,(),A,.,3,a,-,(2,a,-,c,)=3,a,-2,a,+,c,B,.,3,a,+2(2,b,-3,c,)=3,a,+4,b,-3,c,C,.,6,a,+(-2,b,+6)=6,a,+2,b,-6,D,.,(5,x,-3,y,)-
4、(2,x,-,y,)=5,x,+3,y,-2,x,+,y,【解析】,A,.,3,a,-(2,a,-,c,)=3,a,-2,a,+,c,故本选项正确,符合题意,;,B,.,3,a,+2(2,b,-3,c,)=3,a,+4,b,-6,c,故本选项错误,不符合题意,;,C,.,6,a,+(-2,b,+6)=6,a,-2,b,+6,故本选项错误,不符合题意,;,D,.,(5,x,-3,y,)-(2,x,-,y,)=5,x,-3,y,-2,x,+,y,故本选项错误,不符合题意,.,A,2,.,去括号,:-2(3,x,-1)=,_,.,【解析】,-2(3,x,-1)=-6,x,+2,.,-6,x,+2,【
5、重点,2,】,整式的化简及求值,(,模型观念、运算能力,),【典例,2,】,(,教材再开发,P92,例,4,拓展,),已知,A,=2,a,2,-,a,+3,b,-,ab,B,=,a,2,+2,a,-,b,+,ab.,(1),化简,A,-2,B,;,(2),当,a,-,b,=2,ab,=-1,时,求,A,-2,B,的值,;,(3),若,A,-2,B,的值与,b,的取值无关,求,A,-2,B,的值,.,【自主解答】,(1),A,-2,B,=(2,a,2,-,a,+3,b,-,ab,)-2(,a,2,+2,a,-,b,+,ab,),=2,a,2,-,a,+3,b,-,ab,-2,a,2,-4,a,+
6、2,b,-2,ab,=-5,a,+5,b,-3,ab,;,(2),由,(1),得,因为,a,-,b,=2,ab,=-1,所以,A,-2,B,=-5,a,+5,b,-3,ab,=-5(,a,-,b,)-3,ab,=-52-3(-1)=-10+3=-7;,(3),由,(1),得,-5,a,+5,b,-3,ab,=(5-3,a,),b,-5,a,由于,A,-2,B,的值与,b,的取值无关,因此,5-3,a,=0,即,a,=,所以,A,-2,B,=-5,a,=-5,=-,.,答,:,A,-2,B,的值为,-,.,【变式训练】,(,1),化简,:3(,m,-2,n,+2)+(-2,m,-3,n,);,(
7、2),先化简,再求值,:2(3,a,2,+,a,-2,b,)-6(,a,2,-,b,),.,其中,a,与,b,互为相反数,.,【解析】,(1),原式,=,3,m,-6,n,+6-2,m,-3,n,=,m,-9,n,+6,;,(2),原式,=6,a,2,+2,a,-4,b,-6,a,2,+6,b,=2,a,+2,b,因为,a,与,b,互为相反数,所以,a,+,b,=0,所以原式,=2(,a,+,b,)=0,.,【课堂小测（,8,分钟）】,1,.,(2024,汕尾海丰期末,),下列去括号正确的,是,(),A,.,-(-,a,-,b,)=-,a,+,b,B,.,4(,x,+,y,)=4,x,+4,y
8、,C,.a,-3(,b,-,c,)=,a,-3,b,+,c,D,.x,-(4,y,+2,m,)=,x,-4,y,+2,m,【解析】,A,.,-(-,a,-,b,)=,a,+,b,原式不正确,故此选项不符合题意,;,B,.,4(,x,+,y,)=4,x,+4,y,原式正确,故此选项符合题意,;,C,.a,-3(,b,-,c,)=,a,-3,b,+3,c,原式不正确,故此选项不符合题意,;,D,.x,-(4,y,+2,m,)=,x,-4,y,-2,m,原式不正确,故此选项不符合题意,.,B,2,.,若一个多项式加上,5,x,2,-4,x,-3,得到,-,x,2,-3,x,则这个多项式,为,_,.,
9、【解析】,设这个多项式是,A,则,A,+5,x,2,-4,x,-3=-,x,2,-3,x,所以,A,=-,x,2,-3,x,-(5,x,2,-4,x,-3)=-,x,2,-3,x,-5,x,2,+4,x,+3=-6,x,2,+,x,+3,.,-6,x,2,+,x,+3,3,.,(2024,江门恩平质检,),去括号,:5,a,3,-4,a,2,-(,a,-1)=,_,.,【解析】,原式,=5,a,3,-(4,a,2,-,a,+1)=5,a,3,-4,a,2,+,a,-1,.,5,a,3,-4,a,2,+,a,-1,4,.,化简,:(2,a,2,b,-,ab,2,)-2(,ab,2,+3,a,2,
10、b,),.,【解析】,(2,a,2,b,-,ab,2,)-2(,ab,2,+3,a,2,b,),=2,a,2,b,-,ab,2,-2,ab,2,-6,a,2,b,=-3,ab,2,-4,a,2,b.,【课后提升】,【基础练】,1,.,(2024,肇庆怀集期末,),下列去括号正确的,是,(),A,.,-(,a,-1)=-,a,+1,B,.,-(,a,+1)=-,a,+1,C,.,+(,a,-1)=+,a,+1D,.,+(,a,+1)=+,a,-1,【解析】,A,选项,-(,a,-1)=-,a,+1,故该选项符合题意,;,B,选项,-(,a,+1)=-,a,-1,故该选项不符合题意,;,C,选项,
11、+(,a,-1)=,a,-1,故该选项不符合题意,;,D,选项,+(,a,+1)=,a,+1,故该选项不符合题意,.,A,2,.,已知,b,-,a,=10,c,+,d,=-5,则,(,b,+,c,)-(,a,-,d,),的值,为,(),A,.-5B.15C.-15D,.,5,【解析】,因为,b,-,a,=10,c,+,d,=-5,所以,(,b,+,c,)-(,a,-,d,)=,b,-,a,+,c,+,d,=10-5=5,.,D,3,.,一条线段长为,6,a,+8,b,将它剪成两段,其中一段长为,2,a,+,b,则另一段长,为,_,.,【解析】,另一段长为,:(6,a,+8,b,)-(2,a,+
12、,b,),=6,a,+8,b,-2,a,-,b,=4,a,+7,b.,4,a,+7,b,4,.,化简,:,(1)3+3,x,-2(,x,-1);,(2)3(,a,+,b,)-7(,a,-,b,)-5(,a,+,b,)+2(,b,-,a,)+,(,a,+,b,),.,【解析】,(1),原式,=3+(3,x,-2,x,+2)=3+(,x,+2)=3+,x,+2=,x,+5;,(2),原式,=3(,a,+,b,)-7(,a,-,b,)-5(,a,+,b,)-2(,a,-,b,)+,(,a,+,b,)=3(,a,+,b,)-5(,a,+,b,)+,(,a,+,b,)-2(,a,-,b,)-,7(,a,
13、-,b,),=-,(,a,+,b,)-9(,a,-,b,)=-,a,-,b,-9,a,+9,b,=-,a,+,b.,【能力练】,5,.,如果,a,-4,b,=0,那么多项式,2(,b,-2,a,+10)+7(,a,-2,b,-3),的值是,(),A.-1B.-2C.1D,.,2,【解析】,因为,a,-4,b,=0,所以,2(,b,-2,a,+10)+7(,a,-2,b,-3),=2,b,-4,a,+20+7,a,-14,b,-21,=3,a,-12,b,-1,=3(,a,-4,b,)-1,=-1,.,A,6,.,若一个多项式加上,5,a,2,+3,a,-2,得到,2-3,a,2,+4,a,则这
14、个多项式,是,_,.,【解析】,设这个式子为,A,由题意得,:,A,+5,a,2,+3,a,-2=2-3,a,2,+4,a,所以,A,=2-3,a,2,+4,a,-(5,a,2,+3,a,-2),A,=2-3,a,2,+4,a,-5,a,2,-3,a,+2,A,=-8,a,2,+,a,+4,.,-8,a,2,+,a,+4,7,.,先化简,再求值,:2(3,x,+2,y,)+2,x,+2,y,-(,x,-,y,),其中,x,y,满足,|,x,+1|+(,y,-2),2,=0,.,【解析】,原式,=6,x,+4,y,+2(,x,+2,y,-,x,+,y,)=6,x,+4,y,+6,y,=6,x,+
15、10,y,因为,|,x,+1|+(,y,-2),2,=0,|,x,+1|0,(,y,-2),2,0,所以,|,x,+1|=0,(,y,-2),2,=0,所以,x,=-1,y,=2,所以原式,=6(-1)+102=14,.,【培优练】,8,.,(,运算能力、模型观念、应用意识,),(2024,郴州期末,),某校七年级数学兴趣小组发现一组有趣的有理数对,定义如下,:,将两个有理数,m,和,n,称为一组有理数对,记作,m,n,.,若有理数对,m,n,满足,+,=,则称有理数对,m,n,为,“,线性数对,”,.,例如,有理数对,1,-9,即,m,=1,n,=-9,有,+,=,那么,1,-9,就是,“,
16、线性数对,”,.,(1),两组有理数对,-2,18,3,-21,可以称为,“,线性数对,”,的是,_,;,(2),如果有理数对,4,x,是,“,线性数对,”,求,x,的值,;,(3),如果有理数对,a,b,是,“,线性数对,”(,a,0,b,0),求,2(3,b,+9,a,-1)-3(,b,-3,a,-2),的值,.,【解析】,(1),有理数对,-2,18,m,=-2,n,=18,因为,+,=,=,所以,-2,18,为,“,线性数对,”;,同理可求,+,=-,=-,因为,+-,所以,3,-21,不为,“,线性数对,”;,答案,:,-2,18,(2),因为有理数对,4,x,是,“,线性数对,”,所以,+,=,412+4,x,=3(4+,x,),412+4,x,=12+3,x,解得,x,=-36;,(3),因为有理数对,a,b,是,“,线性数对,”,所以,+,=,整理得,9,a,+,b,=0,所以,2(3,b,+9,a,-1)-3(,b,-3,a,-2)=6,b,+18,a,-2-3,b,+9,a,+6=27,a,+3,b,+4=3(9,a,+,b,)+4=4,所以,2(3,b,+9,a,
