# Expanding Brackets

## Expanding Single Brackets

Sometimes, algebraic expression are put into one or more brackets. This can be helpful in some cases, but in other cases we
need to get rid of the bracket(s) to work with the expression. Let us first look at how to expand sing brackets. A single bracket
looks like this . There is a single bracket with one or more numbers of letters inside and a letter or a number in front of
the bracket. To expand (remove) these brackets. We have to multiply the number outside the bracket by the numbers inside. The
example on the right shows how this works. We multiply two by x and 3. Since there is + sign in the middle the expanded
expression is 2x + 3.

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Example 1
To expand the bracket, we have to multiply 3 by a and 3 by
9. Due to the + sign, the solution is 3a + 27.

Example 2
To expand the bracket, we have to multiply a by a and by -b.
Due to the - sign, the solution is a² - ab.

## Expanding Double Brackets

In some cases, we also have double brackets. Instead, of having a number before the bracket, there is
another bracket. Double brackets look like this: . If we want to remove the brackets we have
to multiply the first and second number in the first bracket by both numbers in the second one. The example
on the right show how you have to multiply. The answer to the example would be x²- 5x + 4x - 20 = x² -x -20.
Example 1
To expand the brackets, we have to multiply x and - 6 by
both numbers in the second bracket. This gives us
x² + 7x - 6x - 42 = x² + x - 42 (simplified).

Example 2
To expand the brackets, we have to multiply x and 3 by both
numbers in the second bracket. This gives us
x² + 3x - 3x - 9 = x² - 9 (simplified).

## Check Out Factorisation

After this lesson on expanding brackets, you should attempt to do some factorisation. This is basically the reverse of expanding
brackets as we put an algebraic expression into brackets. You can also select a different topic in our library. Please share this page if
you like it or found it helpful!

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Chapter 14.0: Learning Outcomes
Students will be learn how to expand single brackets!
Students will learn how to expand double brackets!

## VIDEO LESSON:

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