Lesson video

Hi, I'm Mrs Dennett.

And in today's lesson, we're going to be expanding two brackets where there is a negative sign in front of the second bracket.

We have to pay particular attention to this negative sign as we expand and simplify this expression.

We are going to expand each bracket using a multiplication grid.

Eight times x gives us eight x and eight times to give 16.

So we have eight x plus 16.

To expand the next bracket, we have to be aware of the negative four.

Negative four times x is a minus four x and negative four times negative one is positive four.

We now simplify by collecting like terms. We collect the X terms and the number terms to get four X plus 20.

Here's a question for you to try.

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

Here's the answer.

Take care where multiply negative three by negative four in the second bracket, we get positive 12.

Also when simplifying, we get three X takeaway four X, which is negative X and six plus 12 is 18.

So we can write our answer as negative X plus 18 or 18 take away X.

Here's some questions for you to try.

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

Here's the answer.

The questions all look very similar, but you can see that just change in the positive or the negative signs can really impact on your answer.

We always get seven x but the final number and the sign changes.

Here's are some questions for you to try.

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

You have to be so methodical with this question.

There are a lot of negative terms to be aware of.

In part a the negative sign in front of the second bracket means we are just multiplying each term by negative one.

So we get negative four and negative y.

When simplifying the positive four and negative four make zero.

So we are left with minus five y Here's some questions for you to try.

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

Here are the answers.

In question four the second bracket has been multiplied by negative one.

So one and eight g should both be negative.

The final answer should just be 11.

In question five, we have to think about the squared times two.

We even get a negative p squared from the second bracket.

We end up with three terms in our answer after simplifying.

The squared term, a letter term and a number term.

Here's some final questions for you to try.

You will need to use your knowledge of substitution in question six and multiplying fractions in question seven to help you.

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

Here are the answers.

Question six is quite clever.

Did you manage to figure out why we always get an answer of three? If you expand each bracket, you get to two n plus 20, four n minus 20 and minus six n plus three.

Two n add four n take away six n gives us zero.

20 takeaway 20 is zero, add the three and we always get three.

So the value of n doesn't matter because the expression always gives us an answer of three.

I wonder if you could make up some of your own questions like this one.

For question seven, you can see that we collect like terms. They all cancel out to give us zero.

That's all for this lesson.

Thank you for watching.