m4+n 4+(m+n)4因式分解怎么做?

1个回答

  • "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."