Expanding Brackets (Edexcel A-Level Mathematics): Revision Notes
2.5.1 Expanding Brackets
Expanding brackets is a fundamental algebraic technique used to simplify expressions by removing parentheses (brackets) and combining like terms. This skill is essential for solving equations, simplifying expressions, and working with polynomials.
1. Expanding a Single Bracket
When you expand a single bracket, you distribute the term outside the bracket to each term inside the bracket.
General Form:
Example:
2. Expanding Double Brackets
Expanding double brackets involves multiplying two binomials (expressions with two terms). The most common method is the FOIL method (First, Outside, Inside, Last).
General Form:
FOIL Method:
- First: Multiply the first terms from each bracket.
- Outside: Multiply the outer terms.
- Inside: Multiply the inner terms.
- Last: Multiply the last terms.
Example:
- First:
- Outside:
- Inside:
- Last: Combine the results:
3. Expanding with Negative Signs
When dealing with negative signs, be careful with the distribution to ensure correct signs in the expanded expression.
Example:
- First:
- Outside:
- Inside:
- Last: Combine the results:
4. Expanding with More Than Two Brackets
When expanding more than two brackets, expand two brackets first, then multiply the result by the remaining bracket(s).
Example:
- First, expand
- Then, multiply this result by :
Summary:
- Single Bracket: Distribute the outer term across the inner terms.
- Double Brackets: Use the FOIL method to ensure all terms are multiplied correctly.
- Negative Signs: Pay close attention to signs when distributing.
- Multiple Brackets: Expand in pairs, then combine results.