因式分解(3m²-n²)²-(m²-3n²)² 和a
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:2024/08/17 21:40:28
因式分解(3m²-n²)²-(m²-3n²)² 和a²(b-1)+b²-b的三次方
![因式分解(3m²-n²)²-(m²-3n²)² 和a](/uploads/image/z/3525960-48-0.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%883m%26%23178%3B-n%26%23178%3B%EF%BC%89%26%23178%3B-%EF%BC%88m%26%23178%3B-3n%26%23178%3B%EF%BC%89%26%23178%3B+%E5%92%8Ca%26%2317)
(3m²-n²)²-(m²-3n²)²
=[(3m²-n²)+(m²-3n²)][(3m²-n²)-(m²-3n²)]
=(4m²-4n²)(2m²+2n²)
=8(m+n)(m-n)(m²+n²)
a²(b-1)+b²-b³
=a²(b-1)-b²(b-1)
=(b-1)(a²-b²)
=(b-1)(a+b)(a-b)
=[(3m²-n²)+(m²-3n²)][(3m²-n²)-(m²-3n²)]
=(4m²-4n²)(2m²+2n²)
=8(m+n)(m-n)(m²+n²)
a²(b-1)+b²-b³
=a²(b-1)-b²(b-1)
=(b-1)(a²-b²)
=(b-1)(a+b)(a-b)