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Expanding brackets
The rules learned for multiplication in basic algebra can be used in expanding brackets because it involves multiplication of algebraic terms. This section needs to be covered before attempting expanding brackets.
The simplest form of question in this topic is usually a term outside a bracket with two terms inside the bracket. Each term inside the bracket is multiplied by the term outside the bracket as shown in the example below:
Example 1
Firstly the term outside the bracket is multiplied by the first term inside the bracket as shown by the green line. Then the term outside the bracket is multiplied by the second term inside the bracket indicated by the red line. Answer is given after equals sign. Another example is given below:
Example 2
Notice that example 2 the second term inside the bracket is negative or has a negative sign in front of it. So the term outside the bracket (positive) multiplied by the second term inside (negative) gives a negative term.
Exercise 1
1. 2(x + 2)
2. 3(x² + 5)
3. 2x(2x - 6)
4. 4x(x² - 4)
5. 10(x + 5)
6. 8x(x + 7)
7. 5x²(x - 2)
8. 6x(x² - 4)
9. 7(5x + 6)
10.4x²(x² + 5)
Expanding double brackets
Expanding expressions with double brackets requires firstly expanding the brackets by multiplying out terms then simplifying by adding or subtracting the like terms. The example below shows how this is done in two stages.
Example 1
As can be seen by the green lines the first term in the first bracket is multiplied by the first term in the second and then the second term in the second. Then the second term in the first bracket is multiplied by the first term in the second and then the second term in the second shown by the red lines. Once multiplied out in the manner the resulting expression can be simplified as shown below:
Example 2
It is important to be careful of signs when multiplying out. Note in example 2 above there is a negative sign in the second bracket. The result can then be simplified by adding or subtracting like terms as shown below:
Exercise 2
Expand and simplify the following:
