Prove the inequality, if a, B, C are all positive numbers, then (a + b) (B + C) (c + a) ≥ 8abc

Prove the inequality, if a, B, C are all positive numbers, then (a + b) (B + C) (c + a) ≥ 8abc

(a+b)>=2√ab
(a+c)>=2√ac
(c+b)>=2√bc
Because ABC is a positive number, the left and right sides of the inequality are multiplied respectively, and the inequality is proved