作业帮m4+n 4+(m+n)4因式分解怎么做?
来源：学生作业帮 编辑：作业帮 分类：综合作业 时间：2024/05/29 07:26:50
m4+n 4+(m+n)4因式分解怎么做?
"m^4+n^4+(m+n)^4
=m^4+2m^2n^2+n^4+(m+n)^4-2m^2n^2
m^4+n^4+(m+n)^4
=(m^2+n^2)^2-2m^2n^2+(m+n)^4
=[(m+n)^2-2mn]^2-2m^2n^2+(m+n)^4
=[(m+n)^2]^2-4mn(m+n)^2+4m^2n^2-2m^2n^2+(m+n)^4
=2(m+n)^4-4mn(m+n)^2+2m^2n^2
=2[(m+n)^4-2mn(m+n)^2+(mn)^2]
=2[(m+n)^2-mn]^2
=2(m^2+mn+n^2)^2."
=m^4+2m^2n^2+n^4+(m+n)^4-2m^2n^2
m^4+n^4+(m+n)^4
=(m^2+n^2)^2-2m^2n^2+(m+n)^4
=[(m+n)^2-2mn]^2-2m^2n^2+(m+n)^4
=[(m+n)^2]^2-4mn(m+n)^2+4m^2n^2-2m^2n^2+(m+n)^4
=2(m+n)^4-4mn(m+n)^2+2m^2n^2
=2[(m+n)^4-2mn(m+n)^2+(mn)^2]
=2[(m+n)^2-mn]^2
=2(m^2+mn+n^2)^2."