$$ (a+b+c)^3-a^3-b^3-c^3 $$

Question

Uniteasy Admin · Accepted Answer

Extend the cube of binomila identity to trinomial.
$$(a+b)^3 = a^3+b^3+3ab(a+b)$$n
Then,
$$(a+b+c)^3 = (a+b)^3+c^3+3c(a+b)(a+b+c)$$n
Substitute (1) into (2) 
 $$(a+b+c)^3 = a^3+b^3+c^3+3ab(a+b)+3c(a+b)(a+b+c)$$
Then,
$$ (a+b+c)^3-a^3-b^3-c^3 $$
$$ =3ab(a+b)+3c(a+b)(a+b+c)$$
$$ =3(a+b)(ab+ac+bc+c^2) $$
$$=3(a+b)(b+c)(c+a)$$

Question

Answer