[Music] in this video we will identify whether or not an expression is a perfect square trinomial and we will factor perfect square trinomials completely so first identify we have x squared plus two x squared plus y squared so this is a perfect square trinomial later i will explain why and how next 4x squared plus 20x plus 25 this is also a perfect squared trinomial x squared plus 5x plus 6 this is not a perfect square trinomial 9x squared plus 30xy plus 25y squared this is a perfect square trinomial and 4x squared plus 2xy plus y squared this is not a perfect square trinomial okay so how will we know if the given expression is a perfect square trinomial a perfect square trinomial your first term must be a perfect square and it must be positive it's always positive so tatanda and young first term nothing but perfect square shape it's not be nothing perfect square of course we can get its square root okay so young first term nothing positive next the middle term must be twice the product of first and the last term so your middle term nothing multiplying negative dependence are given okay and then next our last term must be a perfect square and it must be always positive so unless terminating just like your first term so to sum it up the first term and the last term must be a perfect square and the positive uh term and then the middle term not then it must be twice the product of first and last term okay let's have an example so eto london buckets a perfect square trinomial so x squared plus 2 x y plus y squared so this is again a perfect square trinomial y so sabi first and last term not in a perfect square and it must be positive so as you can see in the given our first and last term are both positive and then so it's a check nothing perfect squares so first term not in a perfect square also our last term or young story term not m now that path tag me multiply nothing on first and last term at the names not in chasse 2 but the resulting product must be the middle term so 2 times x times y that is 2xy and that is our middle term so therefore this is a perfect square trinomial next 4x squared plus 20x plus 25 so let's see let's see if the our first term and last term are both perfect squares so in 4x squared that is 2x cassette 2 raised to 2 that is 4 and then x raised to 2 that is x squared so 4x squared and then 25 we all know that 25 is a perfect square and that is 5. so 5 squared is 25. now we will multiply the first and the last term so that is 2x and 5 so 2 times 2x times 5 so that is 4x times 5 that is 20x and that makes it a perfect square trinomial next we have x squared plus five x plus six so let's check so our first term is a perfect square our last term or our third term is not a perfect square so six is not a perfect square so dun palang masa sabina hindi is a perfect square trinomial so this is not a perfect square trinomial next number four nine x squared plus 30 x y plus 25y squared so our first term is a perfect square that is 3x and then our third term is a perfect square that is 5y and then we will multiply 3x and 5y so twice so we will have 2 times 3x that is 6x plus 5y that is 30xy and then 4x squared plus 2xy plus y squared so our first term is a perfect square that is 2x our last term is a perfect square also and then we will uh multiply 2x and y and then times 2pa so we will now have 2 times 2 x is equal to 4x times y that is 4xy but as you can see a middle term not indito i 2x y long so this is not a perfect square trinomial so mean middle term that it must be twice the product of your first and last term so that makes it not a perfect square trinomial okay now how to factor perfect square trinomials x squared plus 2xy plus y squared that will become x plus y raised to 2 or simply the quantity of x plus y squared or the square of x plus y all right where x is your first term and then your y here is your last term so dul lang tayo titting in now take note kapagang trinomial nothing or a perfect square trinomial nathan i x squared plus 2 x y kappa middle term net and a positive then young resulting factor is positive then okay negative your middle term the resulting factor is negative then or minus okay so this is now our factored form so again x squared plus 2xy plus y squared but again i'm given a 10 a perfect square trinomial the factoid form is the square of x plus y and then if it's x squared minus 2xy plus y squared the factored form is x minus y squared or the square of x minus y let's have an example so i have here x squared plus 10 x plus 25 so that pattern factored formula or the square perfect square trinomial a perfect square and first and last term net n so x and then five so they are both perfect squares and then we will check if the middle term is twice the product of your first and last term so multiply nothing on x and five sa two so we will have two times x that is two x times five that is ten x and that satisfies our our middle term so e using the square of x plus y because the given expression is a perfect square trinomial so we can now have the factored form just copy the first term which is x and copy that last term which is five that's it as simple as that next i have here 16x squared plus 72x plus 81. so since a middle terminal and i positive or plus therefore the resulting factor or young factory formulating will be the square of x plus y so plus i said the middle term is plus so we will check first if the given expression is a perfect square trinomial case in this a perfect square trinomial we cannot use this form the square of x plus y okay so check nothing on first and last term nothing come perfect square ah perfect square sila so 16x squared is 4x that is a perfect square and 81 is also a perfect square and that is 9 squared so now let's check the middle term if it is twice the product of 4x and 9 okay so 2 times 4x that is 8x times 9 that is 72x and that satisfies our middle term okay so therefore the factored form just copied the first term which is 4x and then our last term which is nine so the factored form is the square of four x plus nine or uh dalawang binomial four x plus nine times four x plus nine okay next i have here x squared minus 22x plus 121. so as you can see the factored form must be x minus y but because our middle term here is minus so that pattern factored formula is square of x minus y okay so before anything else before you proceed let's check first if it's a perfect square trinomial so check nothing first and last term come perfect square so for our first term is x squared so obviously it's a perfect square and our last term is 121 which is 11 squared okay so therefore let us now check the middle term if it's twice the product of your first and last term so we will multiply x and 11 times two so 2x times 11 that is 22 x and that satisfies our middle term so therefore we can now proceed to the factory form just follow the rule okay so we will just copy the first term which is x and then the second term are the last term which is 11. so our factored form is x minus 11 squared next 25 m squared minus 20 m n plus 4 n squared is equal to the square of x minus y so again this is x minus minus because our middle term is minus okay so check first if it's a perfect square trinomial so again we need to check kung perfect square trinomial term 25 m squared so that is 5m that is a perfect square and then 4n squared that is 2n and 2n is a perfect square and no 4n squared is a perfect square and that is 2 at the quantity of 2n raised to 2. and then we will get twice the product of your first and last term which is 5 m into n so 2 times 5 that is 10 m times 2 n that is 20 m n so our factored form will be we will just copy the first and last so that is 5m and 2n so our factored form is the square of 5m minus 2n or the square of the difference of 5m and 2n okay next i have here 27 a squared plus 72 a b plus 48 b squared so now this is an example of an expression which is not a perfect square trinomial because as you can see 27 is not a perfect square also 48 so it is the square of x plus y and the square of x minus y if the given polynomial is a perfect square trinomial in this a perfect square trinomial all you have to do is to factor out okay so pakistan factor out you need to look for the gcf so since and gcf need to a3 so if i factor out nothing sha i know you multiply most of three to get 27a squared that is 9a squared okay and then an imma multiply muscle 3 to get 72 a b so that is 24 a b what will you multiply to 3 to get 48 b squared that is 16 b squared okay so now now factor out nothing sha we can now um factor 9 a squared plus 24 a b plus 16 b squared by it because this is now a perfect square trinomial okay so hapaganito i'm given a hindisha perfect square trinomial try to factor out and then thing resulting from square trinomial okay so since nothing in a perfect square trinomial we can have the factored form three times so again what is thus a square root of 9a squared that is 9a i know 3a and then for 16b squared that is what is the square root of 16 that is 4 and then 4b okay so the factored form is uh 3 times the square of the quantity of 3a plus 4b okay let's have the next one 4x cubed minus 24x squared plus x so we now have since in the ul it's a perfect square we will factor out for x but for x that is the gcf e so what will you multiply to 4x to get 4x cubed that is x squared and then to get 24x squared we will have 6x and then what will you multiply to 4x to get 36x that is 9. okay so check not in nine times four that is 36 and then x okay so we now have the perfect square trinomial so we can now factor so the factored form will be for x times and a young square root x squared that is x and on square root 99 that is 3. so this is our factored form thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button to our walmart channel just keep on watching