解:(1)4a²-b²+4a-2b
=(2a+b)(2a-b)+2(2a-b)
=(2a-b)(2a+b+2)
(2)x²-2xy+y²-1=(x-y)²-1
=(y+l) (x-y-l).
(3) 9x²+6x+ 2y-y²
= (9x²-y²) +(6x+2y)
= (3x+y) (3x-y)+2(3x+y)
(4)x²-y²+a-b²+2ax+2by
=(x²+a²+2ax)-(y²+b²-2by)
=(x+a) ²- (y-b) ²
=[(x+a)+(y-b)][(x+a)-(y-b)]
=(x+a-y+b) (x+a+y-b).