Alright, here goes.

Prove that

abc>(a+b-c)(a-b+c)(-a+b+c)

What I've done:

By AM>GM property,

(a+b+c)/3>(abc)^(1/3)

By AM>GM property, I also found that

(a+b+c)/3>((a+b-c)(a-b+c)(-a+b+c))^(1/3)

From here onwards I'm stuck, since it doesn't really make sense now.

Need help here.

Thanks in advance.