因式分解(x2-b2+y2-a2)2-4(ab-xy)2怎么做?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 05:29:12

因式分解(x2-b2+y2-a2)2-4(ab-xy)2怎么做?
因式分解(x2-b2+y2-a2)2-4(ab-xy)2怎么做?

因式分解(x2-b2+y2-a2)2-4(ab-xy)2怎么做?
(x2-b2+y2-a2)2-4(ab-xy)2
=(x2-b2+y2-a2)2-(2ab-2xy)2
=(x2-b2+y2-a2+2ab-2xy)×(x2-b2+y2-a2-2ab+2xy)
=[(x-y)2-(a-b)2]×[(x+y)2-(a+b)2]
=(x-y+a-b)×(x-y-a+b)×(x+y+a+b)×(x+y-a-b)

用平方差求:
(x²-b²+y²-a²)²-4(ab-xy)²
=(x²-b²+y²-a²+2ab-2xy)(x²-b²+y²-a²-2ab+2xy)
=[(x-y)²-(a-b)²][(x+y)²-(a+b)²]