思维诊断 (打“√”或“× (1)单项式乘多项式时,多项式有几项积就有几项.(√) (2)2xy(2xy-3x2y)=4x2y2-6x3y.(×) (3)(-2m2)(m-n)=2m32m2n.(×) (4)(a-b+c)a=a2-ab+c.( (5)2x(x-y)=2x2-2xy.()
(打“√”或“×”) (1)单项式乘多项式时,多项式有几项,积就有几项.( ) (2)2xy(2xy-3x2y)=4x2y 2-6x3y.( ) (3)(-2m2)(m-n)=-2m3-2m2n.( ) (4)(a-b+c)·a=a2-ab+c.( ) (5)2x(x-y)=2x2-2xy.( ) √ × × × √
棵宪…典创导学 知识点1单项式乘多项式 【例1】计算:(1)(4m)(3m-2n) (2) Xy Xy+=y-X (3)3a2(a3b2-2a)-4a(-a2b)2
知识点 1 单项式乘多项式 【例1】计算:(1)(-4m)(3m-2n). (2) (3)3a2(a3b 2-2a)-4a(-a 2b)2. ( ) 3 2 2 1 3 6xy ( xy y x ). 3 2 − − + −
思路点拨】单项式与多项式相乘→单项式与单项式相乘→计 算结果 【自主解答】(1)(-4m)(3m-2n)=(-4m)3m+(-4m)(-2n) =-12m2+8mn (2)(-6xy3) xy+y-X) =2x2y4-9xy5+6x3y3 (6wy)8)+(6y)1y+(y)(+x)
【思路点拨】单项式与多项式相乘→单项式与单项式相乘→计 算结果. 【自主解答】(1)(-4m)(3m-2n)=(-4m)·3m+(-4m)·(-2n) =-12m2+8mn. (2)(-6xy3) = =2x2y 4-9xy5+6x3y 3. 1 3 2 2 ( xy y x ) 3 2 − + − ( ) ( ) ( ) ( ) 3 3 2 3 2 1 3 6xy ( xy) 6xy y 6xy x 3 2 − − + − + − − g g g
(3)3a2(a3b2-2a)-4a(-a2b)2 =3a2a3b2+3a2(-2a)-4a(a4b2) 3a5b2-6a34a5b2 a5b2-6a3
(3)3a2(a3b2-2a)-4a(-a 2b)2 =3a2·a 3b2+3a2·(-2a)-4a·(a4b2) =3a5b2-6a3-4a5b2 =-a 5b2-6a3