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Multiplying Polynomials - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

There are different methods for multiplying polynomials. One method is to use an area model, but another way to multiply polynomials without having to draw diagrams, is to multiply polynomials using distribution. In order to understand multiplying polynomials, we need knowledge of multiplying monomials and binomials and to know the rules of multiplying exponents.

Multiplying polynomials and basically, what we're doing when multiplying polynomials is expanding a term to a power or even sometimes just a term times a term. You know that when you have x minus 3 squared what you're really doing is x minus 3 times x minus 3. And the word I'm sure you've heard at some point in your Math career is FOIL, first, outer, inner, last and that's fine for sort of the principle behind what's going on but what I want to do is just break that down a little bit more. And basically show you that what you're really doing is taking each term in your first polynomial in this case it's the binomial because there's 2 terms and multiplying it by every term in the other one as well. So what you're really doing is the x times 3 and the x times x and you're also taking the negative 3 times x, and the negative 3 times negative 3 as well.
So you're really taking this x and multiplying it by everything over here and this term here multiplying it by everything as well. Now you're dealing with binomials when you're dealing with something with 2 terms foiling works okay but as we go forward and you're not always going to be dealing with just 2 and 2, FOIL the word it won't hold but the principle still will. Okay so let's finish this out, we have x times x which is just going to be x squared, negative 3 times x, negative 3 times x and negative 3 times negative 3 combining like terms what we actually end up with then is x squared minus 6x+9. So expanding a polynomial to 2 times of polynomial [IB] problem is just a binomial expansion something with 2 terms, FOIL is the word you know but remember that FOIL is actually just standing for the principle of taking each term in 1 polynomial and multiplying it by every other term and the other.

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