# Lesson video

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Hello, I'm Mr. Lund.

And in this lesson, we'll be factorising single brackets.

Factorising is the inverse of expanding brackets.

These two expressions are identical.

One has been factorised, it has a number before some brackets, and the other is the expanded version of the expression.

We can use multiplication grids, to show us how to factorise expressions.

Here I have an expression, four plus 10.

The highest common factor of both those terms is two.

Which two numbers did I multiply to give me the answer of four? That's right, two multiplied by two gives me four.

Which number did I multiply by two, to give me the answer of 10? It's plus five.

Here's an algebraic expression, four a plus 10.

The highest common factor of these two terms, again, is the number two.

Which term did I multiply by two to give me four a? Two a times by two gives me four a.

And then finally, to find this term of the expression, I need to multiply two by five.

So let's have a look at a multiplication grid.

What do you think is the missing number here? That's right, you should have had an answer of two.

Here are some questions for you to try.

Pause the video and return to check your answers.

Here's the solutions to questions one, and number two.

So, in the first example, you had the highest common factor of two, that's highest common factor between six a and 10.

So if you divide both terms by two, you would have found your solutions.

six a divided by two gives three, 10 divided by two gives you five.

The second example was a little bit trickier cause you had less to work off.

But the highest common factor of those two terms is the number five.

Dividing both terms by five, we'll find you the answers that go along the top there.

And then finally, question two, there are no common factors.

And if there are no common factors to two terms, you cannot factorise them, but we'll go on to find out more about factorization, throughout the lesson.

Let's factorise four a plus eight.

First of all, find the highest common factor of these two terms. Then place highest common factor outside a pair of brackets.

Inside brackets, we need two terms, which will multiply by four, to find is the original expression.

But are we sure about this? Let's check by expanding.

Four multiplied by a, four multiplied by two, find the answer four a plus eight.

That's what we started off with, so we have factorised correctly.

Let's have a look at another example.

What's different about this example? Well, it almost looks exactly the same, but there's a negative sign instead of a positive sign.

That means that the highest common factor, again, will be four.

Place four outside of a pair of brackets, and inside our brackets, we need two terms that when multiplied by four, find us the original expression.

Let's check by expanding four times by a, four times by negative two, plus four a negative 8.

Fantastic, we factorise correctly.

Let's have a look at the example we did previously.

And I want to talk about fully factorising your answers.

So, here I have placed two outside of brackets, inside of brackets are placed two a plus four.

If I were to expand these brackets, I would find that they are indeed exactly the same expressions.

But on the right, we have not fully factorised, we didn't find the highest common factor although we picked up find a common factor, you must always fully factorise.

Here is a quick question for you.

The highest common factor of eight a, and 16 is four.

Nope, that's not true.

The highest common factor of 18 and 16 is eight.

Four is a factor of eight a and 16.

But it is not the highest common factor.

Let's look at some more examples.

Let's factorise four a plus 10.

The highest common factor four a plus 10 is two.

If I place two outside of brackets, inside my brackets, I would place two a plus five.

You can check that by expanding I'm going to move on to a different example here.

Here I have 10 a subtract eight.

The highest common factor, again is two.

Let's place that outside a pair of brackets inside our brackets, we need two terms multiplied together to give us the original expression.

There we go.

Check by expanding, I'll leave you to do that.

Notice that although the variable inside those brackets has a coefficient, it has been fully factorised.

And that's why I'd like to show you those examples.

So let's try some factorising.

Find the highest common factor, place it outside of brackets, and then you need two terms inside the brackets that will expand to give you exactly the same expression that you started off with.

Could look, pause the video and return once you want to check your answers.

Here are the solutions to question number three in examples i and j we have more than two terms you can factorise more than two terms, if you can find the highest common factor and there is a common factor between all three terms. In example j there is no common factor.

So it will not factorise it is as it is.

Okay, here's examples four and five, good look.

Pause the video and return to check your answers.

Okay, here are the solutions to questions four and five.

Question five, hopefully you recognise that there was a higher common factor, and the highest common factor of those two terms was four.

Now, one way you could find that solution is by expanding the bracket, and then solve a reimagining the original expression.

And well done for getting this far.

So problem solving questions involving factorization.

Pause the video and return to check your answers.

Here's the solutions to question number six.

If you are looking to find the perimeter of a rectangle and you only have been given the width and the length of that rectangle.

Remember, you need to multiply by two.

And if you look at the factorised form of the perimeter, you see that it is two lots of those two terms three and then seven plus a.