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Hello, everyone.

This lesson is about factorising brackets and we're factoring out letters.

Hello, I'm Mr. Lund.

I'm going to use multiplication grids to show you how factorization works.

Here I have two terms, a squared and a.

Highest common factor of these two terms is a.

Which term did I multiply a by to give me a squared? That's right, it's a.

which term did I multiply a by to give me a? Yes, a times by one just gives you the answer a.

Have a look at this second example.

Here's a multiplication grid.

I'm going to pull out the highest common factor and place it at the front of my multiplication grid.

A multiply by a gives me a squared.

Notice this has a coefficient of two.

A times by two gives me 2a.

So what's the missing factor of this multiplication grid? Did you find it? You should have found plus five.

What is the missing highest common factor from this multiplication grid? Did you find it? It should have been a.

You can check by multiplying three by a, that gives you three a squared.

A times by negative one gives you negative a.

There we go.

So let's back factorise this expression, aA squared plus 8a.

The highest common factor of these two terms is a.

I'm going to write a outside a pair of brackets.

Inside my brackets, I need two terms that will multiply by a to give me the original expression.

There we go.

But let's double check by expanding.

A multiplied by a gives me a squared.

A multiplied by plus eight gives me plus 8a, if my pen works, there me go.

Plus 8a.

We've checked by expanding.

Let's have a look at another example.

How is this example different? First of all, I can see a negative sign.

Secondly, it looks like there is a coefficient of eight on the t squared term.

Nevertheless, the highest common factor of these two terms is t.

Let's write t outside of a pair of brackets.

Inside the brackets we need two terms that will multiply by t to give us the original expression.

Let's double check that.

So t multiplied by 8t gives you 8t squared.

And then I have T multiplied by a negative one finds me an answer of negative t.

We've checked by expanding, so we factorised correctly.

Well done, everyone.

So let's factorise this expression.

It looks a bit more complicated, definitely looks different.

The a squared term is second rather than in the first place.

And there are two negative signs.

Nevertheless, the highest common factor of these two terms can be thought of as being a.

If you factorise a outside of brackets, then inside he brackets you should have negative eight, negative a.

Check by expanding.

For you bright sparks out there, why not try factoring out negative a and see how that changes things.

Interesting task for you.

If you don't want to try that task, here's a second example.

In this example, we have coefficients in front of the t squared term and the t term.

There are no common factors other than the highest common factor of t.

So t goes outside of brackets and inside of brackets I end up with 5t, negative seven.

Check though by expanding.

It's useful to check.

So supercalifragilisticexpialidocious, let's have a go at some examples.

Pause the video and resume once you've finished to check your answers.

Here are the solutions to question number one.

The numbers three and seven are both prime numbers.

So the only common factor between those two numbers is the number one.

Here are some examples for you to try.

Pause the video and return to check your answers.

Here are the solutions to question number two.

In question g and h you had to collect like terms before you could factorise.

For example, b squared plus b plus b can be rewritten as b squared plus 2b.

Here's some more examples for you to try.

Pause the video and return to check your answers.

Here are the solutions to questions three and four.

In questions 4b, if you had substituted a value such as negative one or negative two into those expressions, you'll see that the values of the expressions changes when you, for example, substituted in positive one and positive two.

That will change their order some of the times but not always.

Really well done for getting this far.

Here's the last examples for you to try.

Pause the video and return to check your answers.

Here are the solutions for questions five, six and seven.

In question six, it probably would have been useful to expand all those brackets to find the sequence.

Well, in part two of question six, there are some brackets, but that is not an expanded version of the expression, so watch out for that one.