,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,3.,多项式与多项式相乘,华东师大版 八年级数学上册,3.多项式与多项式相乘华东师大版 八年级数学上册,复习旧知,(1)(-,x,),3,(-,x,),3,(-,x,),5,=_;,(2)(,x,2,),4,=_;,(3)(,x,3,y,5,),4,=_;,(4)(,xy,),3,(,xy,),4,(,xy,),5,=_;,(5)(-3,x,3,y,)(-5,x,4,y,2,z,4,)=_;,(6)-3,ab,2,(-4,a,+3,ab,-2)=_.,-,x,11,x,8,x,12,y,20,x,12,y,12,15,x,7,y,3,z,4,12,a,2,b,2,-9,a,2,b,3,+6,ab,2,复习旧知(1)(-x)3(-x)3(-x)5=_,情境导入,某地区在退耕还林期间，将一块长m米、宽a米的长方形林地的长、宽分别增加n米和b米.用两种方法表示这块林地现在的面积，你知道下面的等式蕴含着什么样的运算法那么吗？,m,n,b,am,bm,an,bn,(,m,+,n,)(,a,+,b,)=,ma,+,mb,+,na,+,nb,a,情境导入 某地区在退耕还林期间，将一块长m米、,(,m,+,n,)(,a,+,b,)=,看成是一个整体,(,m,+,n,),a,+,(,m,+,n,),b,=,m,a,+,na,+,mb,+,n,b,(,m,+,n,)(,a,+,b,)=,+,na,+,n,b,m,a,+,mb,这个等式实际上给出了多项式乘以多项式的法那么:,多项式与多项式相乘，先用一个多项式的每一项分别乘以另一个多项式的每一项，再把所得的积相加.,(m+n)(a+b)=看成是一个整体(m+n)a+(m+n,计算：,1(x+2)(x-3)；,2(2x+5y)(3x-2y).,-3,x,=,x,2,-,x,-6,例,3,=,x,2,+2,x,-6,=6,x,2,=6,x,2,+11,xy,-10,y,2,-10,y,2,-4,xy,+,15,xy,探究新知,计算：1(x+2)(x-3)；2(2x+5y)(3x,计算：,1(m-2n)(m2+mn-3n2),2(3x2-2x+2)(2x+1),1(m-2n)(m2+mn-3n2),=,m m,2,+,mmn,-,m,3,n,2,-2,nm,2,-2,nmn,+2,n,3,n,2,=,m,3,+,m,2,n,-3,mn,2,-2,m,2,n,-2,mn,2,+6,n,3,=,m,3,-,m,2,n,-5,mn,2,+6,n,3,例,4,计算：1(m-2n)(m2+mn-3n2)2(3x2,计算：,1(m-2n)(m2+mn-3n2),2(3x2-2x+2)(2x+1),2(3x2-2x+2)(2x+1),=6,x,3,+3,x,2,-4,x,2,-2,x+,4,x,+2,=6,x,3,-,x,2,+2,x,+2,例,4,计算：1(m-2n)(m2+mn-3n2)2(3x2,(1)(,x,+2,y,)(5,a,+3,b,);,解：,(,x,+2,y,)(5,a,+3,b,),=,x,5,a,+,x,3,b,+2,y,5,a,+2,y,3,b,=,5,ax,+3,bx,+10,ay,+6,by,补充例题,计算,(1)(x+2y)(5a+3b);,(2)(2,x,3)(,x,+4);,解：,(2,x,3)(,x,+4),2,x,2,+8,x,3,x,12,=2,x,2,+5,x,=,12,补充例题,计算,(2)(2x3)(x+4);解：(2x3)(x+,补充例题,计算,(3)(3,x,+,y,)(,x,2,y,),；,解：,(3,x,+,y,)(,x,2,y,),=3,x,2,6,xy,+,xy,2,y,2,=3,x,2,5,xy,2,y,2,补充例题计算(3)(3x+y)(x2y)；解：(3x,1(x+5)(x-7)；,计算：,2(x+5y)(x-7y)；,3(2m+3n)(2m-3n)；,4(2a+3b)2.,随堂练习,=,x,2,-7,x,+5,x-,35,=,x,2,-2,x-,35,=,x,2,-7,xy,+5,xy-,35,y,2,=,x,2,-2,xy-,35,y,2,=4,m,2,+,6,mn-,6,mn-,9,n,2,=4,m,2,-,9,n,2,=4,a,2,+,12,ab+,9,b,2,1(x+5)(x-7)；计算：2(x+5y)(x-7,算一算,:,(1)(2,x,+1)(,x,+3)(2)(,m,+2,n,)(,m,+3,n,),(3)(,a,-1),2,(4)(,a,+3,b,)(,a,3,b,),2,x,2,+7,x,+3,m,2,+5,mn,+6,n,2,a,2,-2,a,+1,a,2,-9,b,2,算一算:2x2+7x+3m2+5mn+6n2a2-2a+1a,(5)(,x,+2)(,x,+3),(6)(,x,-4)(,x,+1),(7)(,y,+4)(,y,-2)(8)(,y,-5)(,y,-3),x,2,+5,x,+6,x,2,-3,x,-4,y,2,+2,y,-8,y,2,-8,y,+15,(5)(x+2)(x+3),课堂小结,多项式乘以多项式，展开后项数很有规律，在合并同类项之前，展开式的项数恰好等于两个多项式的项数的积,.,多项式与多项式相乘，先用一个多项式的,每一项,分别,乘以另一个多项式的,每一项,，再把所得的,积,相加,.,课堂小结 多项式乘以多项式，展开后项数很有规律，在合并,复习旧知,计算以下各式，说说你是怎么想的？,1(am+bm)m；,2(a2+ab)a.,1(am+bm)m,2(a2+ab)a,=,am,m,+,bm,m,=,a,+,b,=,a,2,a,+,ab,a,=,a,+,b,复习旧知计算以下各式，说说你是怎么想的？1(am+bm),新课导入,试,一,试,计算：,1(ax+bx)x；,解 1,x,(,a,+,b,),x=ax,+,bx,所以,(,ax,+,bx,),x=a,+,b,新课导入试一试计算：1(ax+bx)x；解 1,试,一,试,2(ma+mb+mc)m.,m,(,a,+,b,+,c,),m=ma+mb+mc,所以,(,ma+mb+mc,),m=a,+,b,+,c,试一试2(ma+mb+mc)m.m(a+b+c)m=,探究新知,例,2,计算：,1(9x4-15x2+6x)3x,2(28a3b2c+a2b3-14a2b2)(-7a2b),探究新知例2计算：1(9x4-15x2+6x)3x2,1(9x4-15x2+6x)3x,解,9,x,4,3,x,=9,x,4,3,x,-15,x,2,-15,x,2,3,x,+6,x,+6,x,3,x,=(93),x,4-1,-(153),x,2-1,+(63),x,1-1,=3,x,3,-5,x,+2,多项式除以单项式，先用这个多项式的每一项除以这个单项式，再把所得的商相加.,1(9x4-15x2+6x)3x解9x43x=9x4,2(28a3b2c+a2b3-14a2b2)(-7a2b),解,28,a,3,b,2,c,-7,a,2,b,=28,a,3,b,2,c,(,-7,a,2,b,),+a,2,b,3,+,a,2,b,3,(,-7,a,2,b,),-14,a,2,b,2,-14,a,2,b,2,(-7,a,2,b,),=-4,a,3-2,b,2-1,c+,(,a,2-2,b,3-1,)-(-2,a,2-2,b,2-1,),=-4,abc,b,2,+2,b,2(28a3b2c+a2b3-14a2b2)(-7a2,补充例题,计算：,(6,x,n,+2,+3,x,n,+1,-3,x,n,-1,)3,x,n,-1,解：,(6,x,n,+2,+3,x,n,+1,-3,x,n,-1,)3,x,n,-1,=6,x,n,+2,3,x,n,-1,+3,x,n,+1,3,x,n,-1,-,3,x,n,-1,3,x,n,-1,=2,x,n,+2-,n,+1,+,x,n,+1-,n,+1,-,1,=2,x,3,+,x,2,-1,思路归纳,如果除式中字母的指数是多项式，计算时要把它看作一个整体，且要添括号.,【,选自,状元大课堂,】,补充例题计算：(6xn+2+3xn+1-3xn-1)3xn,补充例题,化简：,4(,xy,-1),2,+(,xy,+2)(,xy,-2),xy,解：,4(,xy,-1),2,+(,xy,+2)(,xy,-2),xy,=(4,x,2,y,2,-8,xy+,4+,x,2,y,2,-4),xy,=(5,x,2,y,2,-8,xy,),xy,=20,xy,-32,【,选自,状元大课堂,】,思维点拨 进行整式的混合运算，应按照运算顺序进行化简,.,补充例题化简：4(xy-1)2+(xy+2)(xy-2),随堂练习,1(3ab-2a)a,1.,计算：,2(5ax2+15x)5x,=3,ab,a,-2,a,a,=3,b,-2,=5,ax,2,5,x,+15,x,5,x,=,ax,+3,随堂练习1(3ab-2a)a1.计算：2(5ax2,随堂练习,1.,计算：,3(12m2n-15mn2)6mn,4(x3-2x2y)(-x2),=12,m,2,n,6,mn,-15,mn,2,6,mn,=2,m,-2.5,n,=,x,3,(-,x,2,)-2,x,2,y,(-,x,2,),=-,x+,2,y,随堂练习1.计算：3(12m2n-15mn2)6mn,1(4a3b3-6a2b3c-2ab5)(-2ab2),2.,计算：,解,(4,a,3,b,3,-6,a,2,b,3,c-,2,ab,5,)(-2,ab,2,),=4,a,3,b,3,(-2,ab,2,)-6,a,2,b,3,c,(-2,ab,2,),-,2,ab,5,(-2,ab,2,),=-2,a,2,b,+3,abc+b,3,1(4a3b3-6a2b3c-2ab5)(-2ab2),（,2,）,(,x,2,y,3,-,x,3,y,2,+2,x,2,y,2,),xy,2,解 （,2,）,(,x,2,y,3,-,x,3,y,2,+2,x,2,y,2,),xy,2,=,x,2,y,3,xy,2,-,x,3,y,2,xy,2,+2,x,2,y,2,xy,2,=2,xy,-,x,2,+4,x,（2）(x2y3-x3y2+2x2y2),1(9x4-15x2+6x)3x,解,9,x,4,3,x,=9,x,4,3,x,-15,x,2,-15,x,2,3,x,+6,x,+6,x,3,x,=(93),x,4-1,-(153),x,2-1,+(63),x,1-1,=3,x,3,-5,x,+2,多项式除以单项式，先用这个多项式的每一项除以这个单项式，再把所得的商相加.,课堂小结,1(9x4-15x2+6x)3x解9x43x=9x4,