$$ a(c^2(a+c)-b^2(a+b))-b(c^2(b+c)-a^2(a+b))+c(b^2(b+c)-a^2(a+c)) $$
On simplification I get,
$$ a^3b-a^3c+ac^3-ab^3-c^3b+cb^3 $$
I am not sure on how to proceed further. Is there any shortcut to factorise this quickly & efficiently?
Thanks in advance!
Hint:
$$=a^3(b-c)-a(b^3-c^3)+bc(b^2-c^2)$$
$$=(b-c)\{a^3-a(b^2+bc+c^2)+bc(b+c)\}$$
Now $a^3-a(b^2+bc+c^2)+bc(b+c)=a(a^2-b^2)-c^2(a-b)-bc(a-b)$
Can you take it from here?