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II-A Algebra 9.28

 
 
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II-A Algebra 9.28
by Kevin Song - Monday, August 10, 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.

 
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Re: II-A Algebra 9.28
by Areteem Professor - Monday, August 10, 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?