i didn't get that.

i'll summarize what i want to say.

first we showed that

$\displaystyle \frac{[(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3]}{[(a-b)^3+(b-c)^3+(c-a)^3]}=(a+b)(b+c)(c+a)$ ....(1)

then we showed that

$\displaystyle (a+b)(b+c)(c+a)>8abc$ ......(2)

so we have effectively shown that $\displaystyle \frac{[(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3]}{[(a-b)^3+(b-c)^3+(c-a)^3]}>8abc$

which part, part1 or part2 as labeled above is in doubt??