Formula for multiplication of trinomials

[burritoloco]

Hello,

I'm wondering if there's some nice formula for the expansion of trinomials, like this:

$$\prod_i \left(y + x - a_i\right)$$

or for this:

$$\prod_i \left(x^2 + a_ix - b_i\right)$$

I know for instance that in the case of binomials there is the elementary symmetric polynomials available; thus I wonder if there's anything similar for trinomials. Thank you :)

 

[nickalh]

I haven't seen them frequently enough to make them worth memorizing.

They can get complicated or require lots of detail very quickly. If your professor allows it a computer algebra system, may be EXTREMELY handy.
Try
http://www.wolframalpha.com/input/?i=%28+x^2+%2B+a+*+x%2Bb%29%28+x^2+%2B+c+*+x%2Bd%29

http://www.wolframalpha.com/input/?i=product+(x+y+a_i),+i=1..2

 

[burritoloco]

Thanks nickalh. I eventually found a way to avoid the expansion by doing the problem I was working on differently. My prof said he had seen a formula once but he couldn't recall it now. In this case I can't use the computer as I have an arbitrary amount of trinomials to expand. Algebra softwares give you the pattern for sure, but to write in compact notation one would probably have to use some special types of functions in the style of elementary symmetric polynomials.