因式分解:(c²-b²+d²-a²)²-4(ab-cd)²

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 03:32:47
因式分解:(c²-b²+d²-a²)²-4(ab-cd)²因式分解:(c²-b²+d²-a²)

因式分解:(c²-b²+d²-a²)²-4(ab-cd)²
因式分解:(c²-b²+d²-a²)²-4(ab-cd)²

因式分解:(c²-b²+d²-a²)²-4(ab-cd)²
(c²-b²+d²-a²)²-4(ab-cd)²
=[(c²-b²+d²-a²)+2(ab-cd)][(c²-b²+d²-a²)-2(ab-cd)]
=[(c²-2cd+d²)-(a²-2ab+b²)][(c²+2cd+d²)-(a²+2ab+b²)]
=[(c-d)²-(a-b)²][(c+d)²-(a+b)²]
=(c-d+a-b)(c-d-a+b)(c+d+a+b)(c+d-a-b)