Lesson video

I'm Mrs Dennett and in today's lesson we're going to be looking at expanding and simplifying double brackets where the coefficient of x is greater than one.

Here we have two brackets being multiplied together.

Notice the x term in the first bracket has a coefficient of 3.

We are using a multiplication grid to expand these two brackets.

We have 3x and 1 along the side and x + 2 along the top.

We multiply 3x by x to give us 3x squared, 3x by 2 to get 6x, 1 times x gives us x and 1 times 2 gives us 2.

We can collect like terms, the 6x and x give us an answer of 7x so when we simplify this expression we get 3x squared + 7x + 2.

Here's a question for you to try.

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

Here's the answer.

5x times by x gives us 5x squared.

Collect the like terms 5x and 2x which gives us 7x and the final answer is 5x squared + 7x + 2.

There is another method that we can use to expand double brackets.

We want to multiply each term in the first bracket by each term in the second bracket so we start by multiplying 4s by s and 4s by +5.

This gives us 4s squared + 20s.

Then we multiply 7 by s and 7 by 5.

This gives us 7s + 35.

We simplify the expression to get 4s squared + 20s + 7s add 35 and when we simplify it fuller we get 4s squared + 27s + 35.

Here's a question for you try.

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

Here are the answers.

Be very careful with the negatives in these questions.

Notice that part e results in two squared terms because 6h and -6h make 0.

Finally check your answer to part f.

5y + 3 is being squared so write out this bracket twice before expanding it so you don't miss out on the middle term which is 30y.

Let's apply this skill in a context.

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Here is the answer.

To find the area of a rectangle we have to multiply the length by the width.

We get 15x + 6 + 10x squared + 4x.

Simplifying this to 10x squared + 19x + 6.

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 the expression in question 4 every term in the bracket has a coefficient greater than one and we have two letters a and b.

Expand very carefully, 2a times 2a gives us 4a squared, 2a times 3b gives us 6ab, et cetera and simplify these noting that we have two squared terms in this answer.

In question 5 we have a bracket containing three terms one of which is squared.

Multiply each term in the second bracket by 2r first and then each term by 2 and collect the like terms which are 6r squared and 2r squared giving us 8r squared and -8r + 6r which leaves us with -2r.

You may have simplified your terms in a different order.

That's fine.

As long as you have the correct positives with 2r cubed and 8r squared and the other two terms are negative.

Here is a final question for you to try.

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

Here are Martin and Frank's answers.

Martin has to multiply 3j by 3j.

He should get 9j squared but instead of multiplying the 3s he appears to have accidentally added them to get 6.

He should have 9j squared.

Frank has expanded the first three terms correctly but when multiplying +6 by -5 he's written +30.

This final term should be negative.

That's all for this lesson.

Enjoy the rest of your day and thank you very much for watching.