4a²b²-(a²+b²-1)²

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 23:49:31
4a²b²-(a²+b²-1)²

4a²b²-(a²+b²-1)²
4a²b²-(a²+b²-1)²

4a²b²-(a²+b²-1)²
4a²b²-(a²+b²-1)²
= (2ab+a²+b²-1)(2ab-a²-b²+1)
= [(a+b)²-1][1-(a-b)² ]
=(a+b-1)(a+b+1)(1-a+b)(1+a-b)

4a²b²-(a²+b²-1)²
=[2ab-(a²+b²-1)] [2ab+(a²+b²-1)]
=[2ab-a²-b²+1] [2ab+a²+b²-1]
=[1-(a²-2ab+b²)] [(a²+2ab+b²)-1]
=[1-(a-b)²] [(a+b)²-1]
=(1-a+b)(1+a-b)(a+b+1) (a+b-1)