思维诊断 (打“√”或“×”) (1)两个二项式相乘,积一定是四项式.() (2)(a+3)(a-1)=a2-3.(×) (3)(a+b)(a-b)=a2-b2.() (4)(m+3)(m-4)=m2-m-12.( (5)(x+y)(xy)=x2-xy+y2.() ×
(打“√”或“×”) (1)两个二项式相乘,积一定是四项式.( ) (2)(a+3)(a-1)=a2-3.( ) (3)(a+b)(a-b)=a2-b 2.( ) (4)(m+3)(m-4)=m2-m-12.( ) (5)(x+y)(x-y)=x2-xy+y2.( ) × × √ √ ×
棵究·典例导学 知识点1多项式乘多项式 【例1】计算:(1)(3x-2y)(2a+3b) (2)(x-y)(x2+xy+y2) 思路点拨】多项式乘多项式→单项式乘单项式→合并同类项 →结果
知识点 1 多项式乘多项式 【例1】计算:(1)(3x-2y)(2a+3b). (2)(x-y)(x2+xy+y2). 【思路点拨】多项式乘多项式→单项式乘单项式→合并同类项 →结果
自主解答】(1)(3x-2y)(2a+3b) =3X2a+3x3b+(-2y)2a+(-2y)3b =6ax+9bx-4ay-6by (2)(x-y)(x2+xy+y2) =X X2+Xxy+x y2+(-y)x2+(-y)xy +(-y)y2 x3+*y+xy2-xy-xy2-ys
【自主解答】(1)(3x-2y)(2a+3b) =3x·2a+3x·3b+(-2y)·2a+(-2y)·3b =6ax+9bx-4ay-6by. (2)(x-y)(x2+xy+y2) =x·x 2+x·xy+x·y 2+(-y)·x 2+(-y)·xy+(-y)·y 2 =x3+x2y+xy2-x 2y-xy2-y 3 =x3-y 3
【互动探究】多项式相乘的依据是什么? 提示乘法分配律
【互动探究】多项式相乘的依据是什么? 提示:乘法分配律