Here's a hint.

You probably expanded $(a+b)(b+c)(a+c)$ because (using Vieta' theorem) this is $-t$.

Using the first polynomial, Vieta's theorem also gives us (i) $a+b+c$, (ii) $ab+ac+bc$, and (iii) $abc$, so we want to write $t$ in terms of these expressions. Try multiplying some different sets of two of these terms together (that is, (ii) and (iii) or (i) and (iii), etc.), do any give you something close to your expanded expression above?