I have three sums:
$A_1+A_2+A_3...+A_n = A_{T}$
$B_1+B_2+B_3...+B_n = B_{T}$
$C_1+C_2+C_3...+C_n = C_{T}$
The goal is a function that is: $A_1B_1C_1 + A_2B_2C_2 ...+ A_nB_nC_n = ABC_T$
I'd like to represent $ABC_T$ as a function of $A_T, B_T$ and $C_T$
for example something like:
$ABC_T = A_TB_TC_T - A_TB_T -B_TC_T-A_TC_T$
Is this possible? How do I find out how to do it?
I have tried brute force but I quickly end up with too many a,b and cs on my page :(
Any help appreciated..