$a^2b + abc + a^2c + ac^2 + b^2a + b^2c + abc +bc^2$ factorisation 
I came across this from a university mathematics resource page but they do not provide answer to this.
What I did was this:
$(a^2+b^2+c^2)(a+b+c) - (a^3 + b^3 + c^3) + 2abc$
But I don't think this is the correct solution.
How should I spot how to factorise expression here?
I wish to learn more of this seemingly complex and uncommon algebra factorisation.
Can you recommend me a book or a website for this?
There seem to be only common factorisations when I google.
Many thanks in advance,
  Chris

From What I see
 $$ab(a+c)+ac(a+c)+b^2(a+c)+bc(a+c)=(a+c)(ab+ac+b^2+bc)$$
$$=(a+c)(a(b+c)+b(b+c))=(a+b)(b+c)(a+c)$$
