Multiplying Polynomials - Problem 1

Multiplying polynomials; so we know that when we are multiplying binomials something with two terms times something else with two terms, we can use FOIL, first, outer, inner, last in order to simplify it.

When we have something with a trinomial or anything with more than two terms, FOIL doesn’t quite work except the principle still holds true, okay? And what the main thing is, is we want our term, each term from one of the polynomials and multiply it by every term in the other. So for this case what we want to do is we want to take this x times x², times the 4x and times the -1 and do the exact same thing for this -2.

So what I’m going to do is just take the, I always start with the one that’s smaller if I can, if this is 2 and this is 3, start with the one with two terms and then take the leading term and distribute it into everything. So we get x times x² which is x³, x times 4x which is 4x² and x times -1 which is –x. okay.

Do the exact same thing with the other one. So now we take the -2 and distribute it into all three terms. And what I find makes my life a little bit easier is if I actually line up the same powers in a column, that way when I simplify everything it’s organized for me. So -2 times x² is going to be -2x², lining it up underneath the x². -2 times 4x will give me -8x and -2 times -1 is going to be +2. We then just have to add everything together, x³ rather stays x³, 4x² minus 2x² plus 2x², -x -8x, -9x and then the plus 2 there’s nothing to group it with.

So multiplying a binomial times a trinomial is pretty much the same idea as Foiling except we just have this one extra term we have to deal with, it’s not a big deal, just making sure each term from the first polynomial gets multiplied by each term in the second.