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整式的加减
我们已经学过整式的加减,知道整式的加减可以归结为合并同类项,而合并同类项实际就是合并同类项的系数.因此,进行整式的加减,关键就是把各同类项的系数进行加减.
今天在课外阅读时我又学习了一种新的解决整式加减问题的方法.具体做法如下:如果把两个整式的各同类项对齐,我们就可以像小学列竖式进行加减法一样,来进行整式的加减运算了.
怎样把同类项对齐呢?其实,只要将参加运算的整式按同一字母进行降幂排列(按同一字母的指数从大到小的顺序排列),凡缺项则留出空位或添零,然后让常数项对齐(即右对齐)即可.
例如:计算
时,可以用下列竖式计算:
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22right%22%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmunder+accentunder%3D%22false%22%3E%3Cmrow%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E_%3C%2Fmo%3E%3C%2Fmunder%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
∴
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我尝试用上述方法计算:
.
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtable+columnalign%3D%22right%22%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmunder+accentunder%3D%22false%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmtext%3E%26nbsp%3B%3C%2Fmtext%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo+stretchy%3D%22true%22%3E_%3C%2Fmo%3E%3C%2Fmunder%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr+columnalign%3D%22right%22%3E%3Cmtd+columnalign%3D%22right%22%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E11%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
∴
.
任务: