Question

(ab－1)2＋（a＋b－2）（a＋b－2ab）如何因式分解

Answer 1

取ab=A

a+b=B

则原式=(A-1)^2+(B-2)(B-2A)

=A^2-2A+1+B^2-2AB-2B+4A

=A^2+2(1-B)A+B^2-2B+1

=A^2-2(B-1)+(B-1)^2

=(A-B+1)^2

=(ab-a-b+1)^2

=(a-1)^2(b-1)^2