Lesson video

Hi, I'm Miss Davies.

In today's lesson we're going to be expanding a single bracket.

What does this bar model show? I can see b add four add b add four add b add four.

This could also be written as three lots of b add four, or three bracket b add four close bracket.

These both simplify to three b add 12.

So we can say that three open bracket b plus four close bracket is equivalent to three b add 12.

What does this next bar model show? I can see a add b add five add a add b add five.

We could also write this as two lots of a plus b plus five, or we could write it as two a add two b add 10.

This means that two open bracket a plus b plus five close bracket is equivalent to two a plus two b plus 10.

What does this bar model show? I can see five lots of a plus a plus seven.

We could also write this as five lots of two a plus seven, or five open bracket two a plus seven close bracket.

These are both equivalent to 10 a add 35.

This means that five multiplied by two a plus seven is equivalent to 10 a plus 35.

With this example, Dora notices that this can be written as five times two a and five times seven.

We're going to expand four bracket y plus two.

This means we are multiplying y plus two by four.

This can be shown in a bar model like this.

In total we have got four y add eight.

Let's try it Dora's way.

Four bracket y plus two is equivalent to four multiplied by y add four multiplied by two.

This simplifies to four y add eight.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Make sure that you've multiplied every term in the bracket by the term outside of the bracket.

We're writing an expression to represent the area of this rectangle.

To work out the area of a rectangle, we multiply the base by the height.

With this rectangle it would look like this.

Three multiplied by five s subtract two r.

If we expand this bracket, we get 15 s subtract six r.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

For part a, four multiplied by three x plus six is 12 x add 24.

For part b, we calculated four multiplied by two y minus one, which is 10 y subtract five.

We need to find the missing value from this bracket.

We can see that four multiplied by six gives 24.

What do we multiply four by to get 20 b? 20 b divided by four gives us five b, so this is the missing term.

With this example, we've got two missing terms. Something multiplied by seven y gives 49 y.

49 y divided by seven y is seven, so the term outside of the bracket is seven.

Seven multiplied by something is 63, or 63 divided by seven is our missing term.

63 divided by seven is nine, so this is our missing term.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

To find the missing term in part a, you needed to calculate 12 a divided by three, which is four a.

In part b, you needed to calculate 16 divided by four, which is four.

And in part c, you needed to work out seven multiplied by two b, which is 14 b, and 28 a divided by seven, which is equivalent to four a.

With this example we are expanding and simplifying the expression.

Let's start off by expanding that bracket.

This gives us three e add 15 subtract three.

This then simplifies to three e plus 12.

With this next example, we're going to do the same thing.

We're going to start off by expanding the bracket to get 28 t subtract 35 add two.

This then simplifies to give 28 t subtract 33.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Be sure to multiply all terms in the brackets by the term in front of it before you simplify.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Rosie has made a really common mistake, as she's forgotten to multiply the negative one by four.

In the second question, Clare is d minus five years old.

Ben is twice her age, so we're going to multiply two by d minus five, which is two d subtract 10.

Amir is three years older than Ben, so his age can be written as two d subtract 10 add three, which simplifies to two d subtract seven.

That's all for this lesson.

Thanks for watching.