(m-n)^3+(2m+3n)^3的因式分解
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:2024/07/19 09:30:08
(m-n)^3+(2m+3n)^3的因式分解
![(m-n)^3+(2m+3n)^3的因式分解](/uploads/image/z/313244-44-4.jpg?t=%28m-n%29%5E3%2B%282m%2B3n%29%5E3%E7%9A%84%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
(m-n)^3+(2m+3n)^3
=(m-n+2m+3n)(m^2+n^2-2mn+4m^2+9n^2+12mn-2m^2-mn+3n^2)
=(3m+2n)(3m^2+9mn+13n^2)
=(m-n+2m+3n)(m^2+n^2-2mn+4m^2+9n^2+12mn-2m^2-mn+3n^2)
=(3m+2n)(3m^2+9mn+13n^2)