hi guys it's me teacher going in our today's video we will talk about how to multiply polynomials in this video it is important for you to apply your knowledge about loss of exponents and operations on integers so without further ado let's do this topic in multiplying polynomials i will give you two different properties paramagnetic and autonomous effective so the first property in the biblical senior is that we have the distributive property again distributive property so from the name itself alumni we will distribute something so we have here the representation of your distributive property wherein if you have a times b plus c the product is equal to a b plus ac so hidden by an applied and distributive property in operand distributive property if your multiplier and multiplicand are hindi paradigm number of terms so as you can see we have here a as your multiplier and you'll be symmetric multiplicand in which a toy monomial you will be using distributive property so panabolina so we have here a must be multiplied to b so you need to distribute a a times a it will give you a b as the product and a times c it will give you the product of ac so for you to better understand what is meant by a distributive property or comparison i will give you three examples for this part of our video the first example is that we have 5 times x plus 6 again 5 times x plus six as you can see this one is a monomial and the other is a binomial so again for you to be able to do this kind of topic or for you to overcome this kind of topic you need to apply lots of exponents and your knowledge about the operations on integers so the first thing you need to do is to multiply 5 to x and 5 times x it will give you 5x now for the second thing you need to do you need to multiply again 5 to the other term of your binomial which is 6. so 5 times 6 basically it will give you positive 30 or plus 30. this is the answer for example number one distributive property now let's move on with item number two so we have here a monomial to be multiplied by a binomial in which kapagina means not any distributive property it will become 2 times x sorry 2x times 5x that will give you 10 for the number and for the variable x x times x is equivalent to x squared again 2x times 5x the product is 10 x squared and then we need to distribute 2x to the other term you have 2x times eight it will give you 16 and then x this is the answer for item number two so i hope nah suffers to example nathan you already know or you already grasp the concept of distributive property so let's move on with the third example as you can see the third example is quite complicated because we have the negative signs and you exponents generating variables and medium here apparel don't worry as long as you know how to apply lots of exponents and operations and integers you can do it right so the first one you need to do is that you have the monomial and a trinomial as you can see the simplity property is applicable so you have negative 2 times x squared first you need to multiply negative 2x squared to the first term which is 7x cubed and that will give you a negative answer because negative times positive is negative and then 2 times 7 that is 14. now for the variable part so you have your x and then exponents and three that will give you five hindi multiply again in exponents so next nothing that going is to multiply negative 2x squared to the second term which is 5x squared and that will give you again a negative answer because that is negative times positive so 2 times 5 that is 10 and then for the variable part you have x raised to 4. sir bracket 1 again 4 because we have 2 plus 2 okay and then let's move on with the third term you have negative 2x squared to be multiplied to negative 12. as you can see in the long term stat and ipad has negative so that will give you the product of positive and then 2 times 12 that is 24 and since for elemental variable variable simply copy x squared so the answer is x word now for item number three this is the answer for it you have negative 14x to the fifth power minus 10 x to the fourth power plus 24 x squared now let's move on with the next example or the next method that i will teach you on how to multiply polynomials this time tiana would have a chance for the method but it doesn't literally mean foil anybody terms second terms inner terms and last terms so how to apply for method at the illustration at and we have a plus b times c plus d and that is equivalent to this expression foil method that the new first term stating your letter f that is the first terms you will be multiplying um terminal a times c in your that is your inner terms so b times terms that is i and then for letter l it stands for the last terms i knew the long term since the doula that is b times d so you know nothing so it will give you this expression now for the better and for your better understanding i will give you two examples to apply for method so let's have example number one we have here x minus three times x plus two as you can see in the lone polynomials not in are both binomial so he's sipping a capital method in a gamma method we're multiplying two binomials and actually literally speaking uh logically speaking we're actually using distributive property you will be doing first terms so x times x say your fmo so that is x squared that is x squared now you need to deal with the outer terms you have c x times two that is your o that will give you plus two x now for the inner terms your letter i you have here negative 3x because negative 3 times x is negative 3x now for the last terms you letter l net n you have negative 3 times two that will give you minus six and don't forget now when you are doing foil method k random is simplified lagging the level in second sine third term so combining like terms this will be simplified as x squared minus x minus six this is the product of x minus three times x plus 2 okay so let's move on with the last example applying the foil method we have here 3x plus 2 times x minus 1. so applying foil you have f o i l first terms you have three x times x that will give you three x squared now for the outer terms you have 3x minus 3x times negative 1 that will give you negative 3x now for the inner terms your i that will give you plus 2x and then for the last terms for your l two times negative one their product is negative two and simplifying your inner terms you have 3x squared and that will be negative x or negative 1x minus 2. this is the product of our last example so i hope nana tutorial is out in lesson today and if you have any requests negotiating video you can comment down below now if you're new to my channel don't forget to subscribe hit the subscribe button bell button para updates future uploads again i am teacher gone bye