"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."