Question

分解因式：ab（a+b）2-（a+b）2+1=______．

Answer 1

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

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

=(ab-1)a2+(ab-1)b2+2ab(ab-1)+1

=(ab-1)a2+(ab-1)b2+2(ab)2-2ab+1

=(ab-1)a2+(ab-1)b2+(ab)2+(ab)2-2ab+1

=(ab-1)a2+(ab-1)b2+(ab)2+(ab2-2ab+1)