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In this section we consider how to expand (multiply out) brackets to give two or more terms, as shown below:

3 ( x + 6 ) = 3 x + 18

We will start by revising some negative number operations, then move on to multiplying out the brackets.

Negative number operations

When you expand brackets, you often need to multiply a mixture of positive and negative items.

If you are multiplying two items with the same sign together, the answer is positive.
For example, +2 × +5 = +10 and -2 × -5 = +10

If you are multiplying two items with different signs together, the answer is negative.
For example, +2 × -5 = -10 and -2 × +5 = -10

Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) What is -7 × +4 ?
(b) What is -3 × -6 ?
(c) What is -4 × 9x ?
(d) What is -3(9 - 13) ? [HINT: -3(9 - 13) means -3 × (9 - 13)]

Expanding brackets

Look at the expression below:

-3 ( x - 6 )

To expand the brackets, you need to multiply the part outside the brackets by every part inside the brackets.
In this case you need to multiply -3 by both x and -6. Then we combine the results:

Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Expand the brackets in: -4(x - 3)
(b) Expand the brackets in: -3(9 - x)
(c) Expand the brackets in: 4(2x - 12)

Expanding more complicated brackets

Here is a more complicated expression with brackets to expand:

-5x ( 2x + 6y )

In this case you need to multiply -5x by both 2x and 6y.

Working: -5x × 2x = -5 × 2 × x × x = -10 × x² = -10x² -5x × 6y = -5 × 6 × x × y = -30 × xy = -30xy

Then we combine the results:

Practice Questions
Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) Expand the brackets in: 2x(x + 5)
(b) Expand the brackets in: -4x(x - y)
(c) Expand the brackets in: -7x(3y - 2x)

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the
button to find out whether you have answered correctly. If you are right
then will appear and you should move on to the next
question. If appears then your answer is wrong. Click
on to clear your original answer and have another go.
If you can't work out the right answer then click on
to see
the answer.

You have now completed Unit 8 Section 1

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