Multiplying two trinomials; so the concept between multiplying trinomials is very similar to the concept between multiplying binomials, which you know as FOILING, first, outer, inner, last. The problem with trinomials is we no longer just have a first, outer, inner, last we have a bunch of other things going on. But really all we have to do is take the same principle, take the fact that each term has to be multiplied by each other term and then multiply it out by a similar process.
So what I’m going to do then is starting with my first term, my first polynomial, take the first term and distribute it through each of the three terms in the other polynomial. So what I end up with is x² times x² x to the forth, x² times –x, -x³, x² times 3, 3x², okay. Then just continuing down the line, go to your next term, 2x and then distribute that into the other three terms as well.
And to make my life easier I tend to try to line up the powers on x so that way everything is in the column, makes the life, it’s a little bit easier to simplify. So we have 2x times x² which is 2x³. 2x times –x which is -2x² and then 2x times 3 which is +6x, continuing on down to the last term, 2 times x² 2x², 2 times –x, -2x and then 2 times 3 is 6.
Okay, so now all we have to do is combine like terms, it’s going to be the big addition and now you can see why the columns actually make your life a little bit easier is all we have to do is add down. If we did this in a big long row we have to search for like powers and you get the same answer, just going to be a little bit more work. So we can, we only have one x to the 4th term, -x³, 2x³ is going to be single x³, +3, -2, and +2x² the twos cancel living us with +3x², +6 -2, +4x and plus 6.
So expanding,multiplying trinomials together, the principle is exactly the same as FOILING, we just have a lot more terms that we’re dealing with.