2019版七年級數(shù)學(xué)下冊第一章整式的乘除1.4整式的乘法第3課時教學(xué)課件（新版）北師大版.ppt

4整式的乘法第3課時,【基礎(chǔ)梳理】1.多項(xiàng)式乘以多項(xiàng)式法則多項(xiàng)式與多項(xiàng)式相乘,先用多項(xiàng)式的每一項(xiàng)乘另一個多項(xiàng)式的_,再把所得的積相加.,每一項(xiàng),2.用字母表示=_.,ma+mb+na+nb,3.多項(xiàng)式乘以多項(xiàng)式法則的實(shí)質(zhì)將多項(xiàng)式乘多項(xiàng)式轉(zhuǎn)化為幾個單項(xiàng)式乘積的和的形式.4.拓展:本法則也適用于多個多項(xiàng)式相乘,即按順序先將前兩個多項(xiàng)式相乘,再把乘積和第三個多項(xiàng)式相乘,以此類推.,【自我診斷】1.下列各式中,計(jì)算結(jié)果是x2+7x-18的是()A.(x-1)(x+18)B.(x+2)(x+9)C.(x-3)(x+6)D.(x-2)(x+9),D,2.(x2+ax+8)(x2-3x+b)展開式中不含x3和x2項(xiàng),則a,b的值分別為()A.a=3,b=1B.a=-3,b=1C.a=0,b=0D.a=3,b=8,A,知識點(diǎn)一多項(xiàng)式與多項(xiàng)式相乘【示范題1】計(jì)算:(1)(3a+2)(4a-1).(2)(3m-2n+2)(3m+2n+2).(3)(y-2)(y2+2y+4)-(y2+1)(y-1).,【思路點(diǎn)撥】根據(jù)多項(xiàng)式乘多項(xiàng)式法則進(jìn)行計(jì)算,注意符號處理,合并同類項(xiàng)精確結(jié)果化到最簡.,【自主解答】(1)(3a+2)(4a-1)=12a2-3a+8a-2=12a2+5a-2.,(2)(3m-2n+2)(3m+2n+2)=9m2+6mn+6m-6mn-4n2-4n+6m+4n+4=9m2+12m-4n2+4.,(3)(y-2)(y2+2y+4)-(y2+1)(y-1)=y3+2y2+4y-2y2-4y-8-(y3-y2+y-1)=y3-8-y3+y2-y+1=y2-y-7.,【互動探究】如何化簡-(x-1)2?提示:-(x-1)2=-(x-1)(x-1)=-(x2-x-x+1)=-(x2-2x+1)=-x2+2x-1.,【備選例題】計(jì)算:(1)(-3x+2b)(2x-4b).(2)(a2-a+1)(a+1).(3)(2x+5)(2x-5)-3x.,【解析】(1)(-3x+2b)(2x-4b)=(-3x)2x+(-3x)(-4b)+2b2x+2b(-4b)=-6x2+12xb+4xb-8b2=-6x2+16xb-8b2.,(2)(a2-a+1)(a+1)=a3+a2-a2-a+a+1=a3+1.,(3)(2x+5)(2x-5)-3x=4x2-10 x+10 x-25-4x2+3x=3x-25.,【微點(diǎn)撥】多項(xiàng)式乘以多項(xiàng)式的三點(diǎn)注意1.相乘時,按一定的順序進(jìn)行,必須做到不重不漏.2.多項(xiàng)式與多項(xiàng)式相乘,仍得多項(xiàng)式,在合并同類項(xiàng)之前,積的項(xiàng)數(shù)應(yīng)等于原多項(xiàng)式的項(xiàng)數(shù)之積.3.相乘后,若有同類項(xiàng)應(yīng)該合并.,知識點(diǎn)二多項(xiàng)式與多項(xiàng)式相乘的應(yīng)用【示范題2】(2017深圳勝華學(xué)校質(zhì)檢)若(x2+nx+3)(x2-3x+m)的展開式中不含x2和x3項(xiàng),求m,n的值.,【思路點(diǎn)撥】先利用多項(xiàng)式乘多項(xiàng)式的法則將其展開,然后合并同類項(xiàng),最后根據(jù)要求建立方程靈活解答.,【自主解答】(x2+nx+3)(x2-3x+m)=x4-3x3+mx2+nx3-3nx2+mnx+3x2-9x+3m=x4+nx3-3x3+mx2-3nx2+3x2+mnx-9x+3m=x4+(n-3)x3+(m-3n+3)x2+(mn-9)x+3m,因?yàn)檎归_式中不含x2和x3項(xiàng),所以n-3=0,m-3n+3=0,解得,n=3,m=6.,【互動探究】題目中出現(xiàn)不含x2項(xiàng)類的問題該怎樣理解?提示:不含哪一項(xiàng)意味著展開合并同類項(xiàng)后哪項(xiàng)的系數(shù)為0.,【備選例題】(2016重慶南岸區(qū)長江中學(xué)月考)若(y+3)(y-2)=y2+my+n,則m,n的值分別為()A.m=5,n=6B.m=5,n=-6C.m=1,n=6D.m=1,n=-6,【解析】選D.因?yàn)?y+3)(y-2)=y2-2y+3y-6=y2+y-6,(y+3)(y-2)=y2+my+n,所以y2+y-6=y2+my+n,所以m=1,n=-6.,【微點(diǎn)撥】求多項(xiàng)式乘法中相關(guān)字母的值的兩種題型及思路1.在包含多項(xiàng)式乘多項(xiàng)式的等式中,要確定相關(guān)字母的值:應(yīng)先計(jì)算多項(xiàng)式乘多項(xiàng)式,化簡后與已知多項(xiàng)式對照,對應(yīng)的系數(shù)相等,進(jìn)而求出相關(guān)字母的值.,2.結(jié)果中“不包含某項(xiàng)”,要確定相關(guān)字母的值:先計(jì)算多項(xiàng)式乘多