将下列各式分解因式: (1)x2-9y2 (2)x3-2x2y+xy2 (3)2x(a-b)-(b-a) (4)x2-4y2-3x+6y.
问题描述:
将下列各式分解因式:
(1)x2-9y2
(2)x3-2x2y+xy2
(3)2x(a-b)-(b-a)
(4)x2-4y2-3x+6y.
答
(1)x2-9y2=(x+3y)(x-3y);
(2)x3-2x2y+xy2=x(x2-2xy+y2)=x(x-y)2;
(3)2x(a-b)-(b-a)=(a-b)(2x+1);
(4)x2-4y2-3x+6y=(x+2y)(x-2y)-3(x-2y)=(x-2y)(x+2y-3).