因式分
(1)(a+b)x2-(a+b);
(2)9(a+b)2-4(a-b)2;
(3)6xy2-9x2y-y3;
(4)4+12(x-y)+9(x-y)2.
(1)(a+b)x2-(a+b)
=(a+b)(x2-1)
=(a+b)(x+1)(x-1);
(2)9(a+b)2-4(a-b)2
=[3(a+b)+2(a-b)][3(a+b)-2(a-b)]
=(3a+3b+2a-2b)(3a+3b-2a+2b)
=(5a+b)(a+5b);
(3)6xy2-9x2y-y3
=-y(y2-6xy+9x2)
=-y(3x-y)2;
(4)4+12(x-y)+9(x-y)2
=[3(x-y)+2]2
=(3x-3y+2)2.