因式分解:(1-x²)(1-y²)+4xy
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:综合作业 时间:2024/07/05 06:42:46
因式分解:(1-x²)(1-y²)+4xy
![因式分解:(1-x²)(1-y²)+4xy](/uploads/image/z/15061183-7-3.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9A%EF%BC%881-x%26%23178%3B%EF%BC%89%EF%BC%881-y%26%23178%3B%EF%BC%89%2B4xy)
=1-x²-y²+x²y²+4xy
=1+2xy+x²y²-(x²-2xy+y²)
=(1+xy)²-(x-y)²
=(1+xy+x-y)(1+xy-x+y)
=1+2xy+x²y²-(x²-2xy+y²)
=(1+xy)²-(x-y)²
=(1+xy+x-y)(1+xy-x+y)