hello my name is trisha maurice and i would like to welcome you to my channel mathematics simplex please don't forget to subscribe now today we'll be doing factorizing algebraic expression now what is an expression it is a group of terms put together without an equal sign so when i have something like 5 a squared minus 10 a this is considered to be an expression an expression is without an equal sign so what do we mean by factorizing factorization is when we factor out the highest common factor listen carefully the highest common factor so if we have an expression like this and i see factorized the first thing that i'm expecting you to do is to create a bracket once we have the expression within a bracket it's like we're trying to factor out or in other words take out what is common so what are we going to do we're going to first look at the coefficient of the variable so the coefficient of a squared is 5 and the coefficient of a is 10. so ten and five so i have the five and a ten so i look at these two numbers and i see what is the highest common factor in other words what's the biggest number that can go into these two numbers without leaving a remainder and you should be seeing five so the highest common factor so you should be seeing five so it means i'm going to factor out a five so factoring out the five it means that we can see five into five it goes one times five into ten two times and i can have my sign now we look at the variable now we have a squared and we also have a sale and so we approach the number it is the same way we are going to approach the variable so again we are going to say what is the highest common factor in other words how many a is going to factor out if realize we have a squared remember a squared means a times a so looking at this a square means we have two a's since this a represents we have only one e so again what is the highest common factor and by now looking at this you should be seeing it's a if i factor out an e if i say a squared divided by a because really eventually i'm factoring out an a from the a squared what we can do is divide to find how many a's is left so remember i said a square is a times a so i can cancel this so it means i only have one a here so if i factor this a from the a square i'm left with just an a right here but on the other side if i am factoring out all of these so it means nothing will be left on this side so it means my answer is 5 e and 1 is the same thing as a minus 2. for 5y plus 15 this expression if you realize it doesn't have two variables on either side so this term the 5y has the variable but the next term it just have the constant which is 15. so right away you should be thinking that there's no variable to factor out but i can factor out a number that's common so let me put this within the bracket and i'll be looking at what is my highest common factor so in this case we have 5 and 15 as a numbers that is in this expression and we are seeing that we need to find the highest common factor or the number that both numbers can be divided by so here we have 15 and 25 we're trying to find the highest common factor the highest common factor means the largest number that can go into the two numbers without leaving a remainder so looking at 5 and 15 you should be seeing that the highest common factor is 5. now if i factor out the 5 we have to know divide to see what is left so a good way to see the 5 into 5 goes one times so we left it one y plus five into 15 goes three times now one thing you need to note is that when you factor out a number you can expand and when you expand you should arrive at 5y plus 50. so if i want to test if my answer is correct i will go about seeing 5 times y five y and five times three fifteen so this is correct so it means uh factorizing this expression is five open bracket y plus three okay so here we have an expression five x squared minus thirty x the first thing we're going to look at is what is the highest common factor for the numbers so let us look at positive 5 now you could put negative 30 but i'm going to just put the number 30. now i am just looking at what is the highest common factor so the highest common factor is is the largest number that can go into 5 and 30 without leaving our main loan so you should be able to say it is 5. if we look at the variable x square and x we want the highest common factor for x square and x remember just like when i was doing the activity that says a square the same thing as a times e it's the same case where x squared is the same thing as x times x when you look at x square and x how many variables can i factor out it has to be just x so factorizing these for 5 and 30 i know i can factor out a 5 and for for x square and x i can factor out an x so when i factor out the 5 we can divide each of the number by the number that's factored outside here so five into five it goes one times and five into thirty goes six times if you realize i have the minus sign still because five into thirty goes six times but the sign remains as negative now for the x removal x square means we have two x's in the numerator so we can divide and one of the x cancels or left with x and x x goes one times this will be times one so what we have is five x and one x is the same thing as x minus six so here we have another expression minus two x square minus three x we will be leaving the sign so we just write the number twelve and 3 looking at 12 and 3 we determine the highest common factor so by now you should be saying 3 can go into 12 and 3 without leaving a remainder so my highest common factor is three again we get the variable x square and x so you should be able to quickly see the highest common factor here is a variable x now doing this activity is a little bit different where we have negative signs here when you have negative signs on either side or in other words in front of both coefficients when we have negative signs in front of both terms so this is my first term this is my second term then it means that i can go ahead and factor out what is common i can go ahead and factor all the signs so because these are both negative i can factor the negative sign and then i'll go ahead and write the three and the x no we're going to do the division so remember i factor the minus sign and the highest common factor for the number is 3 and the highest common factor for the variable is x so i'll be dividing the numbers by the minus three so let's do it negative 12 divided by negative three that gives us four and negative three divided by negative three that gives me positive one now we're going to divide the variable by x so i divide x square by x and the x into x so x into x squared just leaves an x i have my 4x and x into x goes one time so this is times one so we have minus three x open brackets four x and one times one gives me one and remember we can always test if this is correct by expanding so negative three times four gives us this negative twelve x times x gives me x square negative three x times positive one will give me negative three x hey guys please don't forget to subscribe to my channel