Lesson video

Hello everyone.

This lesson is on factorising brackets and we're going to be factoring out letters and numbers at the same time.

Hello everyone, I'm Mr. Lund, I just want to start with some mathematical language that we're going to be using during this lesson.

Here is an algebraic term.

The number in front of the X, I'm going to refer to as the coefficient.

I'm going to use multiplication grids to show us how to factorise.

If I look at the multiplication grid below, I can see three A squared plus six A.

The coefficients are shaded in blue.

The highest common factor of three and six is three.

The algebra, A squared and A has a highest common factor of A so the highest common factor of those two terms, three A squared and six A is three A.

Using a multiplication grid, what did I multiply three A by to give me three A squared? What did I multiply three A by to give me six A? Let's have a look at another example.

Here all I've done is flipped the coefficients.

So I've got a six A squared plus three A this time.

My highest common factor is still three A.

And that finds our solutions.

Three A times by two A gives you six A squared.

Three A times by one gives you plus three A.

Quick fire question for you.

What's the missing factor? Did you find it? It should've been plus three.

Here's another.

What is the highest common factor of six A squared minus 15 A? There we go, three A was the highest common factor.

So, here's some questions for you to try.

It you're not quite up to speed of question two yet, don't worry too much.

Pause the video and return to look at your answers.

Easy solutions to questions one and two.

Question one A was false but the correct answer would've been two A, two A was the highest common factor.

B was false again.

The highest common factor of two B squared and six B should've been two B, okay? Let's factorise.

Four A squared plus eight A.

What's the highest common factor of the coefficients four and eight? The highest common factor of the coefficients is four.

What's the highest common factor of A squared and A.

Well the highest common factor of the algebra parts is A.

That means the highest common factor of four A squared plus eight A is four A.

Leave that outside a pair of brackets and inside the brackets, find two terms that when multiplied by four A will give you the original expression.

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

So if I expand four A and I multiply it by A, I get four A squared, and that's good.

And then four A multiplied by plus two gives me plus eight A is that the same? Yeah, that's the same as the first expression.

Let's have a look at another example.

Eight T squared minus four T.

What's the difference compared to the last example? Well we have a negative sign and we have eight on the T squared and a four on the T so it's like the coefficients have been flipped.

Technical term for you there.

What's the highest common factor of the coefficients? Is four again.

What's the highest common factor of the algebra this time? Well, we're using a different letter so the highest common factor is T.

The highest common factor of eight T squared minus four T is four T.

Let's find two terms inside the brackets that when multiplied by four T, find us our original expression.

Let's double check by expanding.

Four T times by two T gives you eight T squared.

Four T multiplied by negative one gives you negative four T.

Good, that is our job done.

We've factorised correctly.

Let's try and factories one more expression for good luck.

So the highest common factor of the coefficients this time is the lovely number two and the highest common factor of algebra is A.

So the highest common factor of eight A squared subtract six A is going to be two A.

We need two terms inside the brackets that when multiplied by two A, find us our original expression.

Let's check by expanding.

I'll do that for you.

Two A multiplied by four A gives me eight A squared and then two A multiplied by negative three gives me negative six A.

Does that match up? Yes, so we've factorised correctly.

Don't forget to always fully factorise.

Is this expression fully factorised? No, in this case it's not.

Inside the brackets here, two X and four have a common factor of two.

Fully factorised, you should've ended up with six X and then inside brackets, X plus two.

Check by expanding.

Yabba dabba do.

Here's some examples for you to try.

Pause the video and come back when you want to check your answers.

Here's the solutions to question number three.

Now, factorising may seem a little bit pointless if you think about it in isolation, but as you get to do more complicated maths, factorising numbers helps to simplify more complicated expressions and it makes your life easier.

Let's try questions four and five.

Pause the video and return to check your answers.

Here are the solutions to questions number four and five.

Question five, hopefully you managed to substitute in, maybe some of you used a calculator.

If you didn't use a calculator, remember to use the order of operations.

Brackets, indices, multiplication or division, addition or subtraction in that order.

Phenomenal.

If you got this far, really well done, well done everyone.

Question six, seven, and eight, pause the video, return to check your answers.

Okay, here's the solutions to question six, seven, and eight.

Question six, being a bit cheeky with one of the expressions cause we factorised out a negative two A but check by expanding.

If you expand those brackets, does it find you and equivalent number card?.