分解因式:m²(n²-1)+4mn-n²+1
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/25 17:42:12
分解因式:m²(n²-1)+4mn-n²+1
![分解因式:m²(n²-1)+4mn-n²+1](/uploads/image/z/18578714-50-4.jpg?t=%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%9Am%26%23178%3B%28n%26%23178%3B-1%29%2B4mn-n%26%23178%3B%2B1)
m²(n²-1)+4mn-n²+1
=m²n²-m²+4mn-n²+1
=﹙m²n²+2mn+1﹚-﹙m²-2mn+n²﹚
=﹙mn+1﹚²-﹙m-n﹚²
=﹙mn+1-m+n﹚﹙mn+1+m-n﹚
=m²n²-m²+4mn-n²+1
=﹙m²n²+2mn+1﹚-﹙m²-2mn+n²﹚
=﹙mn+1﹚²-﹙m-n﹚²
=﹙mn+1-m+n﹚﹙mn+1+m-n﹚