Lesson video

Hi, I'm Mrs. Dennett.

In today's lesson, we're going to be looking at expanding two single brackets and then simplifying.

We need to expand both sets of brackets and then simplify by collecting like terms. We'll look at this with algebra tiles and multiplication grids.

Firstly, we're going to expand each single bracket.

Using algebra tiles, eight, bracket, x plus two would look like this.

In a grid, it looks like this.

So eight times x gives us eight x and eight times two gives us 16.

So we get eight x plus 16.

Next, we expand four, bracket, x minus one.

It would look like this.

Notice the four red tiles which represent negative four.

In a multiplication grid, it would look like this.

We multiply four by x to give us four x and four by negative one to give us negative four.

This gives us four x take away four.

Now, we simplify by collecting like terms. Using the algebra tiles, we can see we have eight x plus four x.

We have four zero pairs, so altogether, we have 12 x plus 12.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you've finished.

Here's the answer.

We get three x plus six and four x take away 12.

We then simplify, collecting the like terms, which are three x and four x, giving us seven x, and six take away 12, which gives us negative six.

Here are some more questions for you to try.

Pause the video to complete the task and restart when you've finished.

Here are the answers.

Although these questions are all very similar, you can see how by just changing the positive sign to a negative sign can really impact your answer.

This is something you need to be really mindful of when expanding and simplifying expressions.

Now we're going to look at what happens when we have an x term outside of the bracket.

In this example, we have eight x outside the first bracket.

Again, we can use multiplication grids to expand each set of brackets.

For the first, we get eight x squared plus 16.

You get this by multiplying eight x by x to give us eight x squared and eight x by positive two to give us positive 16.

For the second bracket, we multiply three by x to give us three x and three by negative one to give us negative three.

This gives us three x take away three.

We now simplify by collecting like terms. The only like terms in this example are 16 x and three x.

We get 19 x when we add these together.

So our final answer is eight x squared plus 19 x take away three.

Here are some questions for you to try.

Pause the video to complete the task and restart when you've finished.

In this set of questions, the position of the numbers and letters varies a lot.

You also need to think about the coefficients.

For example, in part c, we multiply three by two p, not just p, to get six p.

There are also some x squared terms in part d, which we get from multiplying x by x in the first bracket.

Here's a question for you to try.

Pause the video to complete the task and restart when you've finished.

Here is the answer.

When you expand and simplify most of these expressions, you get six x plus six, including from the one at the bottom left, which doesn't contain any brackets.

So you may have reasonably thought that this was the odd one out.

The exception is, in fact, the expression which gives us six x take away two when you expand and you simplify.

Here's a question for you to try.

Pause the video to complete the task and restart when you've finished.

This question highlights how easy it can be to make an error when you're multiplying positive and negative numbers together.

The final answer should be 10 e take away nine d.

We're now going to apply this skill in a different context.

Here, the context is area.

We're going to have to write down an expression for the area of this compound shape.

It is made up of two rectangles.

It helps us to label each triangle, a and b.

I know to find area of a rectangle, I multiply together the length and the width.

So the area of a is n times n, which will be n squared.

The area of b is four times two, bracket, n plus one.

I know that four times two is eight and I can use a grid to help me multiply eight by n plus one.

We get eight n plus eight.

We now need an expression for the total area.

I add together the two expressions.

I need to identify any like terms, but in this case, there aren't any.

So I just write the total area, which is n squared plus eight n plus eight.

Here's a question for you to try.

Pause the video to complete the task and restart when you've finished.

Here is the answer.

You should have labelled each shape a and b.

The area of the top rectangle is given by the expression five n squared take away 10 n.

The area of the bottom pink rectangle is 24 n plus 20.

Add these together and simplify.

That's all for this lesson.

Thank you for watching and remember to take the exit quiz before you leave.