因式分解(1+a²+b²-2a)²-(4b-4ab)(1+a²-b²-
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/05 05:48:40
因式分解(1+a²+b²-2a)²-(4b-4ab)(1+a²-b²-2a)
![因式分解(1+a²+b²-2a)²-(4b-4ab)(1+a²-b²-](/uploads/image/z/4321745-17-5.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%881%2Ba%26%23178%3B%2Bb%26%23178%3B-2a%29%26%23178%3B-%284b-4ab%29%281%2Ba%26%23178%3B-b%26%23178%3B-)
(1+a²+b²-2a)²-(4b-4ab)(1+a²-b²-2a)
原式=[﹙1+a²-2a﹚+b²]²-4b﹙1-a﹚[﹙1+a²-2a﹚-b²]
=[﹙a-1﹚²+b²]²+4b﹙a-1﹚[﹙a-1﹚²-b²]
设 a-1=u
=﹙u²+b²﹚²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+4b²u²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+2×2bu﹙u²-b²﹚+﹙2bu﹚²
=﹙u²-b²+2bu﹚²
=[﹙a-1﹚²-b²+2b﹙a-1﹚]²
=﹙a²-2a+1-b²+2ab-2b﹚²
=﹙a²+2ab-b²-2a-2b+1﹚²
原式=[﹙1+a²-2a﹚+b²]²-4b﹙1-a﹚[﹙1+a²-2a﹚-b²]
=[﹙a-1﹚²+b²]²+4b﹙a-1﹚[﹙a-1﹚²-b²]
设 a-1=u
=﹙u²+b²﹚²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+4b²u²+4bu﹙u²-b²﹚
=﹙u²-b²﹚²+2×2bu﹙u²-b²﹚+﹙2bu﹚²
=﹙u²-b²+2bu﹚²
=[﹙a-1﹚²-b²+2b﹙a-1﹚]²
=﹙a²-2a+1-b²+2ab-2b﹚²
=﹙a²+2ab-b²-2a-2b+1﹚²