Multiplying Out Brackets (Edexcel GCSE Maths): Revision Notes
Multiplying out brackets
When working with algebra, you'll often need to expand brackets by multiplying them out. This process helps simplify expressions and is a fundamental skill you'll use throughout your maths studies.
Expanding brackets is also known as applying the distributive property - a core algebraic concept that forms the foundation for more advanced mathematical operations.
Single brackets
When you have a single bracket, you need to multiply the term outside the bracket by each term inside the bracket. This is called the distributive property.
Key rules to remember
There are several important points to keep in mind when expanding single brackets:
Rule 1: The term outside the bracket multiplies each individual term inside the bracket.
Rule 2: When you multiply letters together, you simply write them next to each other. For example, when you multiply and , you write .
Rule 3: Be careful with powers. Remember that , and means , whilst means .
Rule 4: When there's a minus sign outside the bracket, it reverses all the signs inside when you multiply. This is a common source of mistakes, so be extra careful!
Examples of single brackets
Let's look at some practical applications of these rules:
Worked Example: Expanding Single Brackets
Example 1:
Example 2:
Example 3:
Notice how in the third example, both signs changed because we had a negative outside the bracket.
Double brackets
Double brackets are more complex because you need to multiply everything in the first bracket by everything in the second bracket. This typically gives you four terms initially, which often combine to leave three terms in your final answer.
The FOIL method
The FOIL method is a systematic way to multiply out double brackets:
FOIL Method Breakdown:
- First: multiply the first terms in each bracket together
- Outside: multiply the outside terms (first term in first bracket by second term in second bracket)
- Inside: multiply the inside terms (second term in first bracket by first term in second bracket)
- Last: multiply the last terms in each bracket together
Example of double brackets
Let's apply the FOIL method to a practical example:
Worked Example: Expanding Double Brackets
Expand :
Step 1: Apply FOIL method
- First:
- Outside:
- Inside:
- Last:
Step 2: Combine all terms
Step 3: Simplify like terms
Notice how the two middle terms and combined to give .
Squared brackets
Squared brackets like can be tricky, but there's a safe approach to avoid mistakes.
The key rule for squared brackets: Always write squared brackets as two separate brackets first, then multiply them out using the FOIL method. This prevents common errors.
Example of squared brackets
The safest approach is to treat squared brackets as a special case of double brackets:
Worked Example: Expanding Squared Brackets
To expand :
Step 1: Write as
Step 2: Use FOIL method:
- First:
- Outside:
- Inside:
- Last:
Step 3: Combine:
Common mistake to avoid
Critical Error to Avoid: Don't make the error of thinking . This is wrong because you're missing the middle term that comes from multiplying the two different terms together.
Key Points to Remember:
- The term outside single brackets multiplies every term inside
- A minus sign outside brackets reverses all signs inside
- Use FOIL for double brackets: First, Outside, Inside, Last
- Always write squared brackets as two separate brackets first
- Check your work by ensuring you haven't missed any terms when combining like terms