How to find $abc$ if one is given the values of $a + b + c,$ $a^2 +b^2+c^2, \ a^3+b^3+c^3$ and $ac+bc+ab,$ If I am given the values of $a + b + c,$ $a^2 +b^2+c^2, \ a^3+b^3+c^3$ and $ac+bc+ab,$  how do I find value of $abc \ ?$
I expanded  $(a+b+c)^3$ to get  $a^3+b^3+c^3 + 3(a^2b+a^2c+b^2a+b^2c+c^2a+c^2b) +6abc $ but how do I manipulate $3(a^2b+a^2c+b^2a+b^2c+c^2a+c^2b)$ to obtain a fixed value from it?
Appreciate all advice, thank you. 

The systematic way for this type of problem would be to use Newton' identities, which link Newton's sums: 
$$p_k(x_1,\dots,x_n)=\sum_{i=1}^n x_i^k$$ 
and the elementary symmetric functions:
$$\sigma_k(x_1,\dots,x_n)= \sum_{i_1,\dots,i_n}x_{i_1}\dotsm\, x_{i_n}$$
For $n=3, k=3$, we obtain:
\begin{align*}3abc&=3\sigma_3=\sigma_2p_1-\sigma_1p2+p_3\\
&=(ab+bc+ca)(a+b+c)-(a+b+c)(a^2+b^2+c^2)+(a^3+b^3+c^3),
\end{align*}
which of course is the same as the factorisation given above.
