分解因式: (1)-3ma3+6ma2-12ma (2)18(a-b)3-12b(b-a)2 (3)(2x+y)2-(x+2y)2 (4)-16x4+81y4.

问题描述:

分解因式:
(1)-3ma3+6ma2-12ma
(2)18(a-b)3-12b(b-a)2
(3)(2x+y)2-(x+2y)2
(4)-16x4+81y4

(1)-3ma3+6ma2-12ma=-3ma(a2-2a+4);
(2)18(a-b)3-12b(b-a)2
=18(a-b)3-12b(a-b)2
=6(a-b)2[3(a-b)-2b]
=6(a-b)2(3a-5b);
(3)(2x+y)2-(x+2y)2
=[(2x+y)+(x+2y)][(2x+y)-(x+2y)]
=3(x+y)(x-y);
(4)-16x4+81y4
=81y4-16x4
=(9y2+4x2)(9y2-4x2
=(9y2+4x2)(3y+2x))(3y-2x).