Question 104
Prove that
$$
\frac{a^3(a+c)(a+b)}{(a-c)(a-b)} + \frac{b^3(b+a)(b+c)}{(b-a)(b-c)} + \frac{c^3(c+b)(c+a)}{(c-b)(c-a)} = abc
$$
for all admissible $a$, $b$, $c$ such that $a+b+c=0$.
$$
\frac{a^3(a+c)(a+b)}{(a-c)(a-b)} + \frac{b^3(b+a)(b+c)}{(b-a)(b-c)} + \frac{c^3(c+b)(c+a)}{(c-b)(c-a)} = abc
$$
for all admissible $a$, $b$, $c$ such that $a+b+c=0$.