hey guys in this video I'm going to talk about factorising algebraic expressions so what is factorising well that's to break something into its factors so if you have a number like say 55 for example if you were to factorise 55 you would break it into say think of two factors like 5 times 11 so you've just factorise 55 into 5 times 11 or you could have 1 x 55 and that's a 55 factorised that's actually all of the factors of 55 you can also factorise you can also factorise algebraic term so if you have like 3x well factors of 3x are 3 and x so 3 times x so that's factorising numbers and terms and then if you have an expression well you need to take out the highest common factor so let's have a look at an example so let's say we have 3 lots of x plus 15 and I need to factorise that expression so I need to take out the highest common factor so let's look at 3x factorise that oops so 3x equals 3 times x and then if I factorize 15 well this can be 1 times 15 or it can be 3 times 5 so let's have a look at the factors of 15 that 1 3 5 and 15 so now is there a common factor there yes it's the 3 so that is actually the highest common factor and I need to take that out of this expression and what I mean by take that out well take it out of each term or divide each term by by 3 so what I do with that term that common factor is I put it out the front of the expression and then inside the brackets I need to put some brackets I put the rest of the the expression in those brackets so if I've taking the 3 out of the 3x or divide that by 3 I'm left with x and then if I divide 15 by three you're left with five so that's that expression factorised I've taken out the highest common factor this is useful when you're dealing with fractions and longer terms and equations where it might be easier to factorise and then do some canceling or get rid of some things to simplify an expression so we need to get the hang of this before we move on to more complicated questions all right let's have a look at some more examples okay so you can have all different types of expressions that you can factorise so you might have lots of unknowns so you might have 6ab for example minus a squared b and then you need to factorise that so let's have a look the factors so the factors of 6ab well that's going to be six times a times b and then a squared b it's going to be eight times a times b so can you see any common factors in there well we've got an a here and an a here and we've got a b here and a b here so the highest common factor is actually a combination of a and b so that's going to be a whoops I mean to put that times so the highest common factor is actually ab and then we need to... what goes in the brackets is what's left over in each term so 6ab if we divide that by ab we're just left with 6 I've got a negative and then if we take ab out of a squared b all I'm left with is a okay so and then you can always double check you can expand it back out to make sure you get the same thing so 6ab 6 times ab is 6ab and then ab times a is a squared b so you should end up with what you started with so that's kind of a way to double check that you got the right answer all right ok let's have a look at another example so you can have something that looks like this pqr so for example you might not have any numbers at all you just have lots and lots of letters and you need to decide which letters are the common factors so this looks a bit you know a bit nasty lots of different letters but actually what you really need to do is look for the letters that are common in each term so no "p"s in here so there can't be... I see a q and a q so the q must be a common factor and then r and no r there so the only common factor there must be q so put the q out the front and in brackets it's the letters that are left over so pr and then plus if I taken out q I'm left with an rt and then negative sw all right so that's the factorisation of that expression let's just do a couple more so let's do 25p squared for example minus 10p so now factors of 25p now you need to start possibly you can either write down all the factors or perhaps you can do some working out in your head here and think what's common between 25 and 10 so I know that 5 goes into 25 and 5 goes into 10 but we need the highest is there a higher one I'm not sure so I think it might be 5 that is the highest common factor between 25 and 10 and then and then there's a p squared and a p so actually so p is in both so it's going to be 5p is the common factor and then if you divide 25 by 5 you are left with 5 and then take out a p you've got one p left and then minus 10p divided by 5p well all you're left with is 2 so 10p cancel the "p"s and cancel the 5 and you're left with 2 there okay so hopefully this is all making sense and then just one more example something let's say I don't know you could have higher indices so you might have something like 6p to the power of 4 minus 12p so don't be too afraid of these indices all that's saying is that's four lots of p. p times p times p times p okay so I know that come factor between 6 and 12 or 6 goes into 12 twice so 6 is the highest common factor there and then I've got a p and a p so 6p is the highest common factor and then if I take 6p out of 6p to the power 4 remember that's just p to the power 4 not 6 to the power 4 as well so I've got p to the power of 3 left and then minus 2, 12 divided by 6 is 2 and that p is in the common factor so that's the factorisation of that term 6p bracket p to the 3 minus 2 okay so that's a few examples of factorising algebraic expressions please let me know if there's any details I missed or you need me to go over something that didn't make sense otherwise I will see you next time bye