Question 110
Prove that the inequality
$$
2(a^3 + b^3 + c^3) + abc + ab + bc + ca \ge 2(a^2b + b^2c + c^2a) + a^2 + b^2 + c^2 + a + b + c
$$
holds for all nonnegative real numbers $a$, $b$, $c$.
$$
2(a^3 + b^3 + c^3) + abc + ab + bc + ca \ge 2(a^2b + b^2c + c^2a) + a^2 + b^2 + c^2 + a + b + c
$$
holds for all nonnegative real numbers $a$, $b$, $c$.