把下列各式分解因式：（2x+1)^2-x^2; (x^2+x+1)^2-1; 9(x+y)^2-6(x+y)+1; (x+2)(x-6)+16
问题描述：
把下列各式分解因式：（2x+1)^2-x^2; (x^2+x+1)^2-1; 9(x+y)^2-6(x+y)+1; (x+2)(x-6)+16
请把过程写下来
答
(2x+1)-x =(2x+1+x)(2x+1-x) =(3x+1)(x+1)(x+x+1)-1 =(x+x+1+1)(x+x+1-1) =(x+x+2)(x+x) =x(x+1)(x+x+2)9(x+y)-6(x+y)+1 =[3(x+y)]-6(x+y)+1 =[3(x+y)-1](x+2)(x-6)+16 =x-4x-12+16 =x-4x+4 =(x-2)