八年级数学教案示例：分组分解法

这是一份八年级数学教案示例：分组分解法，共5页。教案主要包含了复习，新课等内容，欢迎下载使用。
八年级数学教案示例：分组分解法　　教学目标1.使学生掌握分组后能运用提公因式和公式法把多项式分解因式;2.通过因式分解的综合题的教学，提高学生综合运用知识的能力.教学重点和难点重点：在分组分解法中，提公因式法和分式法的综合运用.难点：灵活运用已学过的因式分解的各种方法.教学过程设计一、复习把下列各式分解因式，并说明运用了分组分解法中的什么方法.(1)a2-ab+3b-3a;(2)x2-6xy+9y2-1;(3)am-an-m2+n2;(4)2ab-a2-b2+c2.解 (1) a2-ab+3b-3a=(a2-ab)-(3a-3b)=a(a-b)-3(a-b)=(a-b)(a-3);(2)x2-6xy+9y2-1=(x-3y) 2-1=(x-3y+1)(x-3y-1);(3)am-an-m2+n2=(am-an)-(m2-n2)=a(m-n)-(m+n)(m-n)=(m-n)(a-m-n);(4)2ab-a2-b2+c2=c2-(a2+b2-2ab)=c2-(a-b) 2=(c+a-b)(c-a+b).第(1)题分组后，两组各提取公因式，两组之间继续提取公因式.第(2)题把前三项分为一组，利用完全平方公式分解因式，再与第四项运用平方差公式继续分解因式.第(3)题把前两项分为一组，提取公因式，后两项分为一组，用平方差公式分解因式，然后两组之间再提取公因式.第(4)题把第一、二、三项分为一组，提出一个“-”号，利用完全平方公式分解因式，第四项与这一组再运用平方差公式分解因式.把含有四项的多项式进行因式分解时，先根据所给的多项式的特点恰当分解，再运用提公因式或分式法进行因式分解.在添括号时，要注意符号的变化.这节课我们就来讨论应用所学过的各种因式分解的方法把一个多项式分解因式.二、新课例1 把    分解因式.    问：根据这个多项式的特点怎样分组才能达到因式分解的目的?答：这个多项式共有四项，可以把其中的两项分为一组，所以有两种分解因式的方法.解 方法一                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           方法二                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       ;                                                                                                                                                                                                                                                                                                                    例2 把                                                                                                                                                                                                                                                                                                                                                              分解因式.                                                                                                                                                                                                                                                                                                                                                              问：观察这个多项式有什么特点?是否可以直接运用分组法进行因式分解?答：这个多项式的各项都有公式因ab，可以先提取这个公因式，再设法运用分组法继续分解因式.解：                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      =                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    =                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        =                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            =                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                例3 把45m2-20ax2+20axy-5ay2分解因式.分析：这个多项式的各项有公因式5a，先提取公因式，再观察余下的因式，可以按：一、三”分组原则进行分组，然后运用公式法分解因式.解　45m2-20ax2+20axy-5ay2=5a(9m2-4x2+4xy-y2)=5a[9m2-(4x2-4xy+y2)]=5a[(3m2)-(2x-y) 2]=5a(3m+2x-y)(3m-2x+y).例4 把2(a2-3mn)+a(4m-3n)分解因式.分析：如果去掉多项式的括号，再恰当分组，就可用分组分解法分解因式了.解 2(a2-3mn)+a(4m-3n)=2a2-6mn+4am-3an=(2a2-3an)+(4am-6mn)=a(2a-3n)+2m(2a-3n)宋以后，京师所设小学馆和武学堂中的教师称谓皆称之为“教谕”。至元明清之县学一律循之不变。明朝入选翰林院的进士之师称“教习”。到清末，学堂兴起，各科教师仍沿用“教习”一称。其实“教谕”在明清时还有学官一意，即主管县一级的教育生员。而相应府和州掌管教育生员者则谓“教授”和“学正”。“教授”“学正”和“教谕”的副手一律称“训导”。于民间，特别是汉代以后，对于在“校”或“学”中传授经学者也称为“经师”。在一些特定的讲学场合，比如书院、皇室，也称教师为“院长、西席、讲席”等。=(2a-3n)(a+2m).家庭是幼儿语言活动的重要环境，为了与家长配合做好幼儿阅读训练工作，孩子一入园就召开家长会，给家长提出早期抓好幼儿阅读的要求。我把幼儿在园里的阅读活动及阅读情况及时传递给家长，要求孩子回家向家长朗诵儿歌，表演故事。我和家长共同配合，一道训练，幼儿的阅读能力提高很快。要练说，得练听。听是说的前提，听得准确，才有条件正确模仿，才能不断地掌握高一级水平的语言。我在教学中，注意听说结合，训练幼儿听的能力，课堂上，我特别重视教师的语言，我对幼儿说话，注意声音清楚，高低起伏，抑扬有致，富有吸引力，这样能引起幼儿的注意。当我发现有的幼儿不专心听别人发言时，就随时表扬那些静听的幼儿，或是让他重复别人说过的内容，抓住教育时机，要求他们专心听，用心记。平时我还通过各种趣味活动，培养幼儿边听边记，边听边想，边听边说的能力，如听词对词，听词句说意思，听句子辩正误，听故事讲述故事，听谜语猜谜底，听智力故事，动脑筋，出主意，听儿歌上句，接儿歌下句等，这样幼儿学得生动活泼，轻松愉快，既训练了听的能力，强化了记忆，又发展了思维，为说打下了基础。指出：如果给出的多项式中有因式乘积，这时可先进行乘法运算，把变形后的多项式按照分组原则，用分组分解法分解因式.