求解一道数学题；（xy-1)^2+(x+y+2)(x+y+2xy) 分解因式

网友回答

令x+y=a,xy=b原式化为：（b-1）^2+(a+2)(a+2b)=b^2-2b+1+a^2+2a+2ab+4b=b^2+2b+1+a^2+2a+2ab=a^2+2ab+b^2+2a+2b+1=(a^2+2ab+b^2)+2(a+b)+1=(a+b)^2+2(a+b)+1=(a+b+1)^2=(xy+x+y+1)^2=[(x+1)(y+1)]^2=(x+1)^2*(y+1)^2...
======以下答案可供参考======
供参考答案1:
（xy-1)^2+(x+y+2)(x+y+2xy)
=(xy-1)^2+4xy+(x+y)^2+2(xy+1)(x+y)
=(xy+1)^2+(x+y)^2+2(xy+1)(x+y)
=(xy+1+x+y）^2
=(x+1)^2(y+1)^2
供参考答案2:
分解因式：(xy-1)^2+(x+y+2)(x+y+2xy)
设x+y+2=r,x+y+2xy=s
原式=((s-r)/2)^2+rs
=((s+r)/2)^2
=(x+y+xy+1)^2
=(x+1)^2*(y+1)^2