分解因式:(1)4xy2-4x2y-y3;(2)-a+2a2-a3;(3)(x+y+z)2-(x-y-z)2;(4)a2(a-b)2-b2(a+b)2.
答案
(1)-y(2x-y)2;(2)-a(a-1)2;(3)4x(y+z);(4)(a2+b2)(a2-2ab-b2)
知识点:提取公因式法和公式法的综合应用

(1)4xy2-4x2y-y3=-y(4x2-4xy+y2)=-y(2x-y)2;
(2)-a+2a2-a3=-a(a2-2a+1)=-(a-1)2;
(3)(x+y+z)2-(x-y-z)2=(x+y+z+x-y-z)(x+y+z-x+y+z)=(2x)(2y+2z)=4x(y+z);
(4)a2(a-b)2-b2(a+b)2=[a(a-b)+b(a+b)][a(a-b)-b(a+b)]=(a2+b2)(a2-2ab-b2).

因式分解掌握不牢
