Online Course Discussion Forum

II-A Algebra 9.28

 
 
Picture of Kevin Song
II-A Algebra 9.28
by Kevin Song - Monday, 10 August 2020, 3:03 PM
 

Hi, I don't know how to do 9.28. I expanded (a+b)(b+c)(a+c) but i don't know how to factor or solve it. Please help! 

Thanks.

 
Picture of Areteem Professor
Re: II-A Algebra 9.28
by Areteem Professor - Monday, 10 August 2020, 3:50 PM
 

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?