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For more cool math videos visit our site at http://mathgotserved.com or http://youtube.com/mathsgotserved Good day students welcome to mathgotserved.com in this clip were going to be going over how to multiply polynomial expressions or right let's take a look at the first example question number one we are to find the product you going to be find in the product of these two polynomial expressions X +5 multiplied by X square minus 3X +2 okay so in this case we have evenly new binomial be multiply by a quadratic trinomial I want to show you a method that can be used to really facilitate the multiplication of polynomials when you have two or more terms you multiply by three or more terms okay Om what of uses something called the box method isolate go ahead and take use of the box method will do is I'll take the second polynomial expression the one with three terms of quadratic trinomial Lemuel Om the data on the top of the box we have X square minus 3X +2 the terms of this quadratic trinomial will be the Queen determine the columns of my box since I have three terms on when a have three columns my box okay and then we have a binomial Alina binomial there were multiplying by that will go on the left side of the box you have two terms these are determined and normal rules that SO X and then +5 now what we are created is basically the multiplication chart aright just like your typical old-fashioned multiplication charts that you learn how to use in elementary school that's what we accreting here but rather than just multiplying numbers we going to be multiplying variables also okay now before we start multiplying I like to on refresher memory concerning the property of exponents that we are going to be using okay and that is basically the product property of exponents so what happens when you multiply to exponents of the same base so you have X to the am times X to the and what is that the result here using the product property of exponents all you simply do is add the powers X to the am +10 are right values in this Om formula when a make multiplying my polynomial terms okay the keep that in mind okay let's start multiplying so we will have start out by multiplying X and X square remember X have the power of one you don't have to write it there but there so when you multiply X and X square you have the powers in you end up with X to the third power okay if you know want to use the shortcut you can write it out in this multiply count the number exes you multiplying in that will give you the correct result now moving along to the second: the first row X to the first times 3X is negative 3X to the second power there is a one here in just add the two powers in you have X square now last column times XX of the first power times two that is gives us 2X right let's move on to the second row we going to be multiply five by these three terms here five times X square is 5X square five times negative 3X plus times minus is -5 times threes 15 and we have X of the first power is as though there is X to the zero power here and UV out 02 one we just end up with one the last entry involves multiply not two constants five times to is 10 okay okay so now to finish this up we just going to come I like terms the nice in about this method of multiply polynomial's is if you have a lot of terms the box helps you organize your terms so you don't how your terms over the place in you have difficulty combine the like terms is neatly organized for you here okay now exited third does not have any all the like terms to be combined with so we just simply bring that down exited third now if you notice these two terms on this Avenel are like terms the of old second-degree Om variables in the variable X okay so you have 5X square minus 3X squared of the like terms which is combine across the coefficients okay so 5-3 is to so plus 2X square you take a look at the next Avenel we have to like terms nicely organize for you again so just simply combine them longest Avenel this is it the first-degree terms in terms of X so we just combine the coefficients and that add on the X of the first power so what is -15+2 signs a different so's track and keep the sign of the bigger so you have -13 X in the constants down the lonely the have any all the constants to be combined with so we just drop down 10+10 okay so this is our final answer the product of the linear binomial X +5 in the quadratic trinomial X square -10 X +3 right now let's take a look at another example in this case number two we are to expand the linear binomial X Om plus why X was why three's to the fifth power actually dismisses the polynomial so you have X was why recent the fifth power so the method I'm going to be using is the possible triangle you can do this by writing down five Om X to live and then distribution them to out a time Bell take a long-term and it's very inefficient and the chances of making errors is pretty high okay so the best
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