1、多項(xiàng)式與多項(xiàng)式相乘,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.,練一練： (1) (2x+1)(x+3) (2) (m+2n)(m+3n) (3) ( a 1)2 (4) (a+3b)(a 3b ) (5) (x+2)(x+3) (6) (x4)(x+1) (7) (y+4)(y2) (8) (y5)(y3),答案: (1) 2x2+7x+3; (2) m2+5mn+6n2; (3) a22a+1; (4) a29b2 (5) x2+5x+6; (6) x23x4; (7) y2+2y8; (8) y28y+15.,(x+2)(x+3) = (x-4)(x+1) = (y

2、+4)(y-2) = (y-5)(y-3). =,觀察上述式子，你可以得出一個(gè)什么規(guī)律嗎？,(x+p)(x+q) =,拓展與應(yīng)用,x2 + (p+q) x + p q,x2 + 5x+6;,x2 3x-4,y2 + 2y-8,y2- 8y+15,根據(jù)上述結(jié)論計(jì)算： (1) (x+1)(x+2)= (2) (x+1)(x-2)= (3) (x-1)(x+2)= (4) (x-1)(x-2)=,x2+3x+2,x2-x-2,x2+x-2,x2-3x+2,(x+p)(x+q) = x2 + (p+q) x + p q,拓展與應(yīng)用,確定下列各式中m與p的值: (1) (x+4)(x+9) = x2 +

3、 m x + 36 (2) (x-2)(x-18) = x2 + m x + 36 (3) (x+3)(x+p) = x2 + m x + 36 (4) (x-6) (x-p) = x2 + m x + 36 (5) (x+p)(x+q) = x2 + m x + 36,(1) m =13,(2) m = - 20,(3) p =12, m= 15,(4) p= 6, m= -12,(5) p = 4,q = 9, m =13,p=2,q = 18, m=20,p = 3, q =12, m=15,p=6, q= 6, m=12,拓展與應(yīng)用,(x+p)(x+q) = x2 + (p+q) x

4、+ p q,(p，q為正整數(shù)),例2：計(jì)算：,(4)(x+2)(x+3)-(x+6)(x-1),例3：解方程 (1)（2x+3)(x-4)-(x+2)(x-2)=x2+7 (2) (3x-2)(2x-3)=(6x+5)(x-1)-1,例5：（x2+ax+b）（2x2-3x-1）的積中，x3的系數(shù)為-5，x2的系數(shù)為-6，求a、b.,變式練習(xí)：,課堂練習(xí),1、計(jì)算：,(5) (x+y)(2xy)(3x+2y).,2、如果a2a=1,那么求(a5)(a6)的值,課堂練習(xí),小 結(jié),1、多項(xiàng)式與多項(xiàng)式相乘,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.,2、多項(xiàng)式與多項(xiàng)式相乘時(shí)，多項(xiàng)式的每一項(xiàng)都應(yīng)該帶上它前面的正負(fù)號。多項(xiàng)式是單項(xiàng)式的和，每一項(xiàng)都包括前面的符號，在計(jì)算時(shí)一定要注意確定各項(xiàng)的符號。,4、在數(shù)學(xué)知識的學(xué)習(xí)中，“轉(zhuǎn)化”思想是的重要思想方法。在今天的學(xué)習(xí)中，第一步是“轉(zhuǎn)化”為多項(xiàng)式與單項(xiàng)式相乘，第二步是“轉(zhuǎn)化”為單項(xiàng)式