Factorising | GCSE Maths | Third Space Learning

Foreign. Hi, this is Paul from Third Space Learning and today let's look at factorizing. Now, factorizing is just the opposite of expanding brackets. As usual, I'll be using our online classroom to go through the topic and some questions. Look out for links at the end of the video for access to loads of free resources, more practice questions and information on our one to one practice. Personalized maths Tuition There are a few different ways we can factorize. So let's start by factorizing into a single bracket. Grab a pen and let's dive straight in. To factorize into a single bracket, all we have to do is look at the highest common factor of each of the terms. So for example, if we have 3x 6, the highest common factor of both terms is 3. So let's write 3 outside of a pair of brackets. Now we can work out what goes in those brackets by multiplying out. So 3 multiplied by x is 3 x and 3 multiplied by positive 2 is positive 6. So 3 x plus 6 fully factorized is just 3 bracket x plus 2 close bracket. Let's have a look at a few exam style questions to see how this works. So the question says fully factorise 4x, subtract 8. So let's start off by working out the highest common factor of both of those terms. Well, that's just four. So we can write four outside of a pair of brackets. Now, to work out what goes in those brackets, we need to think about what four can multiply by to give each of those terms. So 4 multiplied by something is 4x. Well, that's just x 4 multiplied by x is 4x. In a similar way, let's think about what 4 multiplied by would give negative 8. Well, 4 multiplied by negative 2 is negative 8. So like us there. And there we go. We have fully factorized 4x take away 8. Now the good news about this is we can make sure we've got it right by expanding these brackets. So 4 multiplied by X is 4 X and 4 multiplied by negative 2 is negative 8 and it's worth one mark. Here's another question for you. Have a go, pause the video and see how you get on. So the question says fully factorize 12, take away 3A. Well, we need to first of all think about what the highest common factor of 12 and take away three is. Well, that's just going to be three. So we can write three outside of a pair of brackets. Now we need to think about what will go inside the brackets. So three multiplied by something is 12. Well, that something is just four. So we can put a four there. And then in a similar way, three multiplied by something is negative 3A. Well, that's just going to be negative a. And I can go there. And there we go, fully factorized. So let's pop that on the answer line. So it's really nice and clear. And the good news is we could make sure that this is fully correct. So let's expand these brackets. 3 times 4 is 12 and 3 times negative A is negative 3A. And again, this is worth one mark. Let's have a go at this one. Now, it says fully factorize 6x squared plus 9x. So let's think about what each of these terms actually means. Well, 6x squared means 6 multiplied by x multiplied by x and 9x means 9 multiplied by x. So in the same way, we want the highest common factors. Well, we can see we've got an X x there and an X there. So that X can come to the front of a pair of brackets. Now, there aren't any more letters in common in both of those terms, but we do have some numbers. We have a six and we have a nine. Well, the biggest number that will go into six and nine is three. Three into six goes twice and three into nine goes three times. Now, there isn't anything else I can do. So let's put this all together. 3x open a bracket. And this first term here is going to be 2x. Because 3x multiplied by 2x is 6x squared. And we can see that here 2x. Let's look at the second term. Now, 3x multiplied by something is. Is positive 9x. Well, that's just going to be positive 3. So let's pop that on the anti 3x bracket. 2x plus 3 and we can make sure that this is fully correct. So 3x multiplied by 2x is 6x squared. So that works. And 3x multiplied by 3 is plus 9x. So that's great. This is worth two marks, so we have to be really careful. Two marks is for the full final answer. Now, you would get one mark if you only partially factorized it. So say you forgot to bring out a three or an x. As long as the rest of it was right, you'd still get a mark. So two marks for this question. Here's another exam style question. Pause the video and see how you get on. Okay, let's go through this. Now we've got fully factorised and it's 4x squared y plus 8x. So let's think about what this means. Well, 4x squared y means 4 multiplied by x multiplied by x multiplied by y. And the 8x means 8 multiplied by x. So let's think about what we have in common here. Well, I can see we've got an X here and an X here. So we can bring that out as a common factor and open a pair of brackets. Now are there any more letters that we can bring out to the front? I don't think so, but there are some numbers. So we have a 4 and an 8. So what's the highest common factor of 4 and 8? Well, that's going to be 4. 4 goes into 4 once and 4 goes into 8 twice. Let's fill in the brackets. So 4x multiplied by something is 4x squared y. Well that's just going to be 1 times x times y, 1 times x times y which is just xy. And in a similar way, 4x multiplied by something is positive 8x. Well that's just going to BE positive 2. And let's pop that on the answer line. 4x bracket xy plus 2. Now it's worth 2 marks and we can make sure we've got the answer right here because 4x multiplied by xy is 4x squared y and 4x multiplied by 2 is positive 8x. Again, this is worth 2 marks. 2 marks for the fully correct answer. Now you'll only get one mark if you have not fully factorized it. So again, be super careful about bringing out everything you need to to the front. Thanks so much for watching the video. Thanks. Check out the description below for loads more information on this topic and for access to our library of free online resources and loads of information on our one to one tuition. Don't forget to like and subscribe to stay up to date with all the latest third Space learning videos.