Question 10
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that for all real numbers $a, b, c$, we have
$$
f(a + b + c)f(ab + bc + ca) - f(a)f(b)f(c) = f(a + b)f(b + c)f(c + a).
$$
$$
f(a + b + c)f(ab + bc + ca) - f(a)f(b)f(c) = f(a + b)f(b + c)f(c + a).
$$