Lesson video

Hi, I'm Miss Davies.

In today's lesson, we're going to look at expanding a single bracket that involves squares and cubes.

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Well done if you said that x multiplied by x is written as x squared.

To expand m multiplied by m plus two, we're going to start off by multiplying m by m, which gives us m squared.

We are then going to multiply m by positive two, which is positive two m.

So m multiplied by m plus two is equivalent to m squared add two m.

In the second example we're multiplying four a by a subtract three.

Going to start off by multiplying four a by a, which is four a squared.

Then multiply four a by negative three.

This gives us negative 12 a.

So four a multiplied by a subtract three is equivalent to four a squared subtract 12 a.

Here are some questions for you to try.

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Here are the answers.

Remember that y multiplied by y is y squared.

In question two, Alex has said that x squared multiplied by x is just x squared, but it isn't, it's x cubed.

In these examples we are expanding the brackets.

For the first question, we're going to start off by multiplying m by m squared.

This gives us m cubed.

Next we're going to multiply m by positive two m.

This gives us positive two m squared.

In the next example, the first thing we're going to do is multiply that four a squared by a, which gives us four a cubed.

We're then going to multiply four a squared by negative three.

This gives negative 12 a squared.

So four a squared multiplied by a minus three is equivalent to four a cubed subtract 12 a squared.

Here are some questions for you to try.

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Here are the answers.

Remember that e squared multiplied by e is e cubed.

In question four, for part a we needed to calculate 27 w divided by three w, which is equivalent to nine, which is the missing term.

In part b, eight a cubed divided by by four a is two a squared.

And in part c, you needed to work out the term outside of the bracket.

To do this, you needed to work out 15 g squared divided by three g, which is equivalent to three g.

You can then multiply three g by three h to work out the second missing term, which is nine gh.

With these examples we're expanding a bracket and simplifying the overall expression.

For this question we're going to start off by expanding the bracket.

We're going to multiply three e by e squared add three e.

This gives three e cubed add nine a subtract three e squared add four.

This simplifies to three e cubed add six e squared add four.

This is the final answer, as it cannot be simplified any further.

For the next example we're going to expand the bracket, so we're going to multiply seven t squared by four t subtract five and then add two t.

The bracket expands to 28 t cubed subtract 35 t squared.

This expression cannot be simplified any further, as there are no like terms. Here are some questions for you to try.

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Here are the answers.

Be sure to multiply all of the terms within the bracket by the term in front of it before simplifying the expression.

In this question we're going to find the area of 2D shapes.

This will help you with the next set of question.

This is a parallelogram.

To find the area of a parallelogram, we multiply the base by the perpendicular height.

This is the distance that goes directly up from the base at 90 degrees.

In this question our base is 15 centimetres and our height is six centimetres.

This gives us 90 centimetres squared.

Our next shape is a trapezium.

To find the area of a trapezium, we need to add the parallel sides, multiply that by the perpendicular height, and then divided it by two.

In this example our two parallel sides are 15 centimetres and 25 centimetres.

Our perpendicular height is six.

This is the same as 40 multiplied by six divided by two, or 240 divided by two, which gives us 120 centimetres squared.

Here are some questions for you to try.

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Here are the answers.

For part b, we needed to multiply three x by five x plus three.

This gives 15 x squared plus nine x millimetres squared.

For part b, it was a little bit longer.

You needed to do seven x squared as three x add six.

This gives 10 x squared add six.

We can then multiply this by the perpendicular height, which was three x.

This gives 30 x cubed add 18 x.

The final step is to divide both terms by two.

This gives an answer of 15 x cubed add nine x centimetres squared.

That's all for this lesson.

Thanks for watching.