因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2
问题描述：
因式分解（1）x^2+2xy-x-y+y^2-2 (2) x^2-2xy+3x-3y+y^2+2
答
1.x^2+2xy-x-y+y^2-2
=x^2-1+y^2-1+xy-x+xy-y
=(x+1)(x-1)+(y+1)(y-1)+x(y-1)+y(x-1)
=(x+y+1)(x-1)+(x+y+1)(y-1)=(x+y+1)(x+y-2)
2.x^2-2xy+3x-3y+y^2+2
=x^2-1+y^2-1+x-xy-y-xy+2x+2-2y+2
=(x+1)(x-1)+(y+1)(y-1)-x(y-1)-y(x+1)+2(x+1)-2(y-1)
=(x+1)(x-y+1)+(y-x-1)(y-1)=(x-y+1)(x-y+2)