x²-2xy-2x+y²+2y+1

x²-2xy-2x+y²+2y+1
x²-2xy-2x+y²+2y+1

x²-2xy-2x+y²+2y+1
x²-2xy-2x+y²+2y+1
=（x²-2xy+y²)-2(x-y)+1
=(x-y)²-2(x-y)+1
=[(x-y)-1]²
=(x-y-1)²

原式=(x²-2xy+y²)-2x+2y+1
=(x-y)²-2(x-y)+1
=(x-y-1)²

x²-2xy-2x+y²+2y+1
= x²-2xy+y²-2x+2y+1
= (x-y)²-2(x-y)+1
= (x-y-1)²

原式=(x-y-1)2括号外面是个平方！

x²-2xy-2x+y²+2y+1=x²-2x(y+1)+y²+2y+1=x²-2x(y+1)+(y+1)²=[x-(y+1)]²=(x-y-1)².