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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!
Linear Equations Factorisation Quadratic Equations
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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!

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