Introduction to Factorising Difference of Squares


As the name says it’s pretty much the difference of two squares. If it’s a difference of two different types of squares, you can apply this method. So when I mean this I mean a squared minus b squared, so some number squared minus another number squared. If you have that and make sure it’s always a minus, if it’s in that form, you can make it a plus b, a minus b or you could have an a minus b, a plus b doesn’t really matter about the order.

So that’s pretty much the whole idea. Trying to look at that and that’s what we’re going to be using throughout the next few questions, okay? So, this is the thing, you look at two different types of squared, a squared minus b squared then this a and this b, I can put a plus b, a minus b. So no cross method is required here, you can just go straight to use that formula, okay?

So, let’s try. So, see how x squared minus 25? Well, it’s minus, so we can probably apply that method if it’s a plus, you can’t apply that method. But because it’s a minus, probably we could.
Have a look! We’ve got x squared, that’s a square number, isn’t it? Because it’s x squared. What about 25? Can we make that into a square number?

We know that 25 is 5 squared, isn’t it? So I can change this to x squared minus 5 squared. So it’s in that form, a squared minus b squared, isn’t it? So what do we do? Remember how a squared minus b squared is a plus b, a minus b. So in this case a is x and b is going to be our 5. So, we go x plus 5, x minus 5, just like that. That’s the idea! So it’s very simple, wasn’t it?


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