<s>[INST] $a^2b + abc + a^2c + ac^2 + b^2a + b^2c + abc +bc^2$ 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
 [/INST] $$a^2b+abc+a^2c+ac^2+b^2a+b^2c+abc+bc^2$$
$$=ab(a+b+c)+ac(a+b+c)+b^2c+bc^2$$
$$=(a+b+c)(ab+ac)+bc(b+c)$$
$$=a(a+b+c)(b+c)+bc(b+c)$$
$$=(b+c)[a(a+b+c)+bc]$$
$$=(b+c)[a^2+ab+ab+bc]$$
$$=(b+c)[a(a+b)+c(a+b)]$$
$$=(b+c)(a+b)(a+c)$$
This is the simplest method I could think of. Hope it helps. 
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