# Formula for multiplication of trinomials

• burritoloco
In summary, the conversation discusses the possibility of a formula for expanding trinomials and the use of computer algebra systems to handle complex calculations. The speakers also mention the potential usefulness of elementary symmetric polynomials in writing compact notation for expansions.
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 :)

Last edited:
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

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.

## 1. What is the formula for multiplying trinomials?

The formula for multiplying trinomials is (ax + b)(cx + d) = acx2 + (ad + bc)x + bd.

## 2. How do you multiply trinomials using the FOIL method?

The FOIL method stands for First, Outer, Inner, Last. You multiply the first terms, then the outer terms, inner terms, and last terms, and then combine like terms. For example, (x + 2)(x + 3) = x2 + 3x + 2x + 6 = x2 + 5x + 6.

## 3. Can you provide an example of multiplying trinomials using the box method?

Yes, for (2x + 3)(x + 4), you would create a box with 2 columns and 2 rows. In the top left box, write 2x, and in the bottom right box, write 3. In the top right box, write x, and in the bottom left box, write 4. Then, multiply across the columns and rows to get the final answer of 2x2 + 11x + 12.

## 4. What is the difference between multiplying binomials and trinomials?

The main difference is the number of terms being multiplied. Binomials have 2 terms, while trinomials have 3 terms. The process for multiplying is similar, but with trinomials, you must multiply each term by every other term, rather than just the two terms in a binomial.

## 5. Can you use the distributive property to multiply trinomials?

Yes, you can use the distributive property to multiply trinomials. For example, (3x + 4)(x2 + 2x + 5) can be rewritten as 3x(x2 + 2x + 5) + 4(x2 + 2x + 5). Then, you can use the FOIL method to multiply each term and combine like terms to get the final answer of 3x3 + 10x2 + 23x + 20.

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