课件人教实验版八年级上册15243整式的乘法——多项式的乘法.ppt

多项式乘以多项式,探究,a (m+n)+ b(m+n,(a+ b) (m +n）,am+ bm+ an+ bn,长为 a+b 宽为 m+nS = (a+ b) (m +n）,am,an,bn,bm,S = am+ bm+ an+ bn,a (m+n),b (m+n),m (a+b),n (a+b),S= a (m+n)+ b(m+n),S=m (a+b)+ n (a+b),S = (a+ b) (m +n）,S = am+ bm+ an+ bn,S= a (m+n)+ b(m+n),S=m (a+b)+ n (a+b),(a+ b) (m +n） = a (m+n)+ b(m+n) =m (a+b)+ n (a+b) = am+ bm+ an+ bn,归纳,(a+b)(m+n),=,am,多项式的乘法,+an,+bm,+bn,多项式与多项式相乘，先用一个多项式的每一项乘另一个多项式的每一项，再把所得的积相加.,(a+ b+c) (m +n） =am+an+bm+bn+cm+cn,例1、计算（1）（3x+1)(x-2） (2) (x - 8y)(x-y),法则的应用,解 ：（ 1）原式=3 x2- 6x+x - 2 =3x2- 5x- 2 (2) 原式=x2- xy -8xy +8y2 =x2- 9xy +8y2,(3) (x+y)(2xy)(3x+2y).,(1) (x+y)2 (2) (x+y)(x2y+y2),例2、计算,解：（1) 原式=（x+y）（x+y) =x2+ xy+ xy+ y2 =x2+ 2xy+ y2 （2）原式=x3y+ xy2+x2y2+y3 ( 3 ) 原式=（2x2-xy+2xy-y2)(3x+2y ) = (2x2+xy-y2)(3x+2y) = 6x3+4x2y+3x2y+2xy2-3xy2-2y2 =6x3 + 7x2y-xy2-2y2,() (2a+b)2;,() (x1)(x2+x+1) ;,练习,1.计算,练习: (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) (x-4)(x+1) (7) (y+4)(y-2); (8) (y-5)(y-3),答案: (1) 2x2+7x+3; (2) m2+5mn+6n2; (3) a2-2a+1; (4) a2-9b2 (5) x2+5x+6; (6) x2-3x-4; (7) y2+2y-8; (8) y2-8y+15.,(x+2)(x+3) = x2 + 5x+6; (x-4)(x+1) = x2 3x-4 (y+4)(y-2) = y2 + 2y-8 (y-5)(y-3). = y2- 8y+15,观察上述式子，你可以 得出一个什么规律吗？,(x+p)(x+q) = x2 + (p+q) x + p q,练习： 确定下列各式中m的值:(1) (x+4)(x+9) = x2 + m x + 36(2) (x-2)(x-18) = x + m x + 36(3) (x+3)(x+p) = x + m x + 36(4) (x-6) (x-p) = x + m x + 36(5) (x+p)(x+q) = x + m x + 36 (p，q为正整数),(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,小 结,(a+ b) (m +n）= am+ bm+ an+ bn,(a+ b+c) (m +n）= am+an+bm+bn+cm+cn,多项式与多项式相乘，先用一个多项式的每一项乘另一个多项式的每一项，再把所得的积相加.,多项式与多项式相乘的法则:,(x+p)(x+q) = x2 + (p+q) x + p q,