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Hi, I'm Ms. Davies.

In this lesson, we're going to be multiplying a linear expression by a quadratic expression.

We're going to expand this bracket.

To expand a bracket, we're multiplying x squared by x subtract three.

Let's multiply x squared by x first.

This gives us x cubed.

Next, we're going to multiply x squared by negative three.

This gives us negative three x squared.

x squared multiplied by x subtract three is equivalent to x cubed subtract three x squared.

Let's have a look at this next one.

Five x squared multiplied by x is equivalent to five x cubed.

Five x squared multiplied by negative three is equivalent to negative 15 x squared.

Our final example, let's starts off by multiplying three x squared by x.

This is equivalent to three x cubed.

Three x squared multiplied by negative three y gives us negative three x squared, y.

Only the x is being squared, so the squared only goes on the x term.

Finally, three x squared multiplied by four is positive 12 x squared.

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.

You can check if your answer is correct by factorising it.

If you factorise your answer, you should get the original question.

This time, we're expanding two brackets.

I have written x plus three multiplied by x squared add four in a grid.

We're going to start off by doing x multiplied by x squared.

This is x cubed.

Next, we're going to multiply three by x squared, which is positive three x squared.

Next, we're going to multiply x by four, which is positive four x.

And finally, positive three, multiply by positive four, which is positive 12.

We cannot simplify this expression, so it's our final answer.

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 fully simplified your answers where you can.

Here is a question for you to try.

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

Here is the answer.

To find the volume of this cuboid, you need to multiply x by one of the two lengths.

If we multiply x by x subtract three, this gives us x squared subtract three x.

We're then going to multiply this by the other length.

So, x cubed subtract three x multiplied by four add x, gives an answer of x cubed add x squared subtract 12 x centimetres cubed.

That's all for this lesson.

Thanks for watching.