Page3第十四章整式的乘法與因式分解14.1整式的乘法14.1.4整式的乘法(第3課時(shí))學(xué)習(xí)目標(biāo)1.理解多項(xiàng)式乘法的法則,并會(huì)進(jìn)行多項(xiàng)式乘法的運(yùn)算.2.經(jīng)驗(yàn)探究多項(xiàng)式乘法的法則的過(guò)程,使學(xué)生感受數(shù)學(xué)與生活的聯(lián)系,同時(shí)感受整體思想、轉(zhuǎn)化思想、數(shù)形結(jié)合思想,并培育學(xué)生的抽象思維實(shí)力.學(xué)習(xí)過(guò)程一、自主學(xué)習(xí)1.計(jì)算:(1)-2x2·3xy2;(2)-2x(1-x);(3)x(4x2+x);(4)4x22.結(jié)合上題回憶單項(xiàng)式乘以單項(xiàng)式,單項(xiàng)式乘以多項(xiàng)式的法則各是什么?二、深化探究問(wèn)題1:計(jì)算:(y+2)(4x2+x).問(wèn)題2:類比上題計(jì)算:(a+b)(p+q)問(wèn)題3:你能歸納多項(xiàng)式乘以多項(xiàng)式的法則嗎?問(wèn)題4:已知某街心花園有一塊長(zhǎng)方形綠地,長(zhǎng)為a米,寬為p米.若將原長(zhǎng)方形綠地的長(zhǎng)增加b米,寬增加q米,你能用幾種方法求出擴(kuò)大后的長(zhǎng)方形綠地的面積?三、鞏固練習(xí)【例題】計(jì)算:(1)(3x+1)(x-2);(2)(x-8y)(x-y);(3)(x+y)(x2-xy+y2); (4)(x-y)2.四、深化提高1.計(jì)算(1)(2x+1)(x+3);(2)(q+2n)(q+3n);(3)(a-1)2; (4)(a+3b)(a-3b);(5)(x+2)(x+3); (6)(x-4)(x+1);(7)(y+4)(y-2); (8)(y-5)(y-3).反思:依據(jù)上述(5)~(8)求解過(guò)程,視察所計(jì)算各題有什么共同特點(diǎn),結(jié)果的各項(xiàng)系數(shù)與原式中的系數(shù)有怎樣的關(guān)系?2.口答:(1)(x+2)(x+5);(2)(x-1)(x+4);(3)(x+2)(x-2);(4)(x-5)(x-6);(5)(x+5)(x+5);(6)(x-5)(x-5).3.先化簡(jiǎn)再求值:(9-2y)(9+3y-y2)-y(2y2),其中y=2.五、反思小結(jié)(1)本節(jié)課學(xué)習(xí)了哪些主要內(nèi)容?(2)在運(yùn)用多項(xiàng)式與多項(xiàng)式相乘的法則時(shí),你認(rèn)為應(yīng)當(dāng)留意哪些問(wèn)題?(3)舉例說(shuō)明在探究多項(xiàng)式與多項(xiàng)式相乘的法則的過(guò)程中,體現(xiàn)了哪些思想方法?參考答案一、自主學(xué)習(xí)1.(1)-6x3y2(2)-2x+2x2(3)4x3+x2(4)36x3-4x2-9x2.略二、深化探究1.4x2y+xy+8x2+2x2.法1:(a+b)(p+q)=a(p+q)+b(p+q)=ap+aq+bp+bq法2:(a+b)(p+q)=(a+b)p+(a+b)q=ap+bp+aq+bq3.多項(xiàng)式乘以多項(xiàng)式,先用一個(gè)多項(xiàng)式的每一項(xiàng)乘另一個(gè)多項(xiàng)式的每一項(xiàng),再把所得的積相加.4.法1:(a+b)(p+q)法2:pa+pb+qa+qb法3:(p+q)a+(p+q)b法4:p(a+b)+q(a+b)三、練習(xí)鞏固解:(1)(3x+1)(x-2)=(3x)·x+(3x)·(-2)+1·x+1×(-2)=3x2-6x+x-2=3x2-5x-2.(2)(x-8y)(x-y)=x2-xy-8xy+8y2=x2-9xy+8y2.(3)(x+y)(x2-xy+y2)=x3-x2y+xy2+x2y-xy2+y3=x3+y3.(4)(x-y)2=(x-y)(x-y)=x2-2xy+y2.四、深化提高1.(1)2x2+7x+3(2)q2+5nq+6n2(3)a2-2a+1(4)a2-9b2(5)x2+5x+6(6)x2-3x-4(7)y2+2y-8(8)y2-8y+152.(1)x2+7x+10(2)x2+3