Expanding a single bracket

Expanding a Single Bracket

Introduction

• The process of expanding a bracket involves removing the bracket by multiplying the term outside the bracket with each term inside the bracket.

• This is an essential skill in algebraic manipulation.

The Expand Rule

• Any term (a single number or a variable) outside the bracket is to be multiplied by each term inside the bracket.

• Always remember the signs of the numbers in case of subtraction or negative numbers.

Step-by-Step Guide for Expanding Single Brackets

1. Identify the term outside the bracket and terms inside the bracket.

2. Proceed by multiplying the term outside the bracket with each term inside the bracket individually.

3. If there is more than one term inside the bracket, write each result separately, connecting with a plus or minus sign as per the sign of the terms inside the bracket.

4. Verify your result by using the distributive law, which states that multiplication is distributive over addition or subtraction.

Examples

• In the expression 5(x - 3), 5 is the factor outside the bracket that needs to be multiplied with both x and -3 separately. The expanded form would thus be 5x - 15.

• In the example -2(a - 4), -2 multiplies with ‘a’ and ‘-4’ separately resulting in -2a + 8, noticing that the double negative becomes positive.

Conclusion

• Mastering the skill of expanding single brackets is crucial for more complex algebraic manipulation in mathematics.

• Regular practice of expanding single brackets with varying difficulty levels is recommended. Remember to observe the signs!