因式分解(ab-1)^2+(a+b-2)(a+b-2ab)

(ab-1)^2+(a+b-2)(a+b-2ab)
=(ab-1)^2+(a+b)^2-2(ab+1)(a+b)+4ab
=a^2b^2-2ab+1+4ab+(a+b)^2-2(ab+1)(a+b)
=a^2b^2+2ab+1+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2+(a+b)^2-2(ab+1)(a+b)
=(ab+1)^2-2(ab+1)(a+b)+(a+b)^2
=[(ab+1)-(a+b)]^2
=(ab+1-a-b)^2