In-Depth Look: How to Use Common Factors to Factorise ()

Factorise using Common Factors and Indices


This term and this term what is common? What is the common factor? Can you guys see that a plus b is it in both of them? So a plus b is common. So we take the a plus b out the front like that. So we took a plus b, so we just have from this term. We just have the two left so that’s why I have two there and in this term, because we took the a plus b out we just have the a left which goes there. Get the idea?

So again this is one term and this is another term. From these two terms, what is common? What’s the common factor? Well at the moment I can’t see anything common. There’s nothing common. We have a minus 2b but here we have 2b minus a where they look almost the same but they’re not the same right because of the signs. This is positive a and this is negative a this is negative 2b but this is positive 2b. So they’re the same but opposite signs.

So how can I work with this? I’ll show you a trick here guys. I’m going to try and make these the same because as you can see the only difference is the signs. This one has opposite signs of this one, so what I’m going to do is take a negative out from here, so if I take a negative out negative see how we already have a negative there.

So negative negative will become a positive, so because we took the negative out of this positive 2b will become negative 2b and this negative a will become positive a, so I made it the same a minus b, so a minus 2b, a minus 2b where that changes to a positive. So now you can see that from this term and this term a minus to b is common. I’ll use a different color to see how a minus 2b is common, so now we have a common factor.

Take that a minus 2b outside and we’ll now just have x left here and y left here, so a minus 2b times x plus y okay?

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