Factorize the expression P(a,b,c) = a3(b-c) + b3(c-a) + c3(a-b).

Step 1: Identify the expression and check for factors.
The expression to factorize is $P(a,b,c) = a^3(b-c) + b^3(c-a) + c^3(a-b)$.
This is a cyclic expression.
If we substitute $a=b$ into the expression:
$P(b,b,c) = b^3(b-c) + b^3(c-b) + c^3(b-b)$
$P(b,b,c) = b^3(b-c) - b^3(b-c) + c^3(0)$
$P(b,b,c) = 0$.
Since $