ExamSolutions Maths

Pure

# Prior Knowledge - Expanding Brackets

🤓 Study

📖 Quiz

Play audio lesson

Prior Knowledge - Expanding Brackets

Prior Knowledge - Expanding Brackets

Basic Principles

- Expanding brackets involves
**multiplying**every term inside the bracket by the factor outside the bracket. - It is based on the
**distributive property**in algebra which states that a*(b+c) = a*b + a*c. - When dealing with
**double brackets**, apply the**FOIL method**(First, Outer, Inner, Last) for expansion. - Brackets can also consist of
**more than two terms**. Each term must be multiplied by the term outside the bracket.

Different Kinds of Brackets

**Linear brackets**e.g. 3(x + 2) result to a**linear expression**.**Quadratic brackets**(two brackets with linear expressions) i.e. (x + a)(x + b) transforms into a**quadratic expression**.**Cubic brackets**i.e. (x + a)(x + b)(x + c) expand into a**cubic expression**.

Special Cases

**Square of a binomial**: (a + b)² = a² + 2ab + b²; and (a - b)² = a² - 2ab + b².**Difference of squares**: a² - b² = (a + b)(a - b). It is crucial to memorise this identity.

Practical Applications

**Expanding brackets is critical**in simplifying algebraic expressions and equations.- They are heavily used in factorising, completing the square and solving quadratic equations.
**Polynomial division**or**long division**is also an area where expanded brackets come into play.- It's useful in calculus, specifically in finding the derivative using the
**Product Rule**.

Common Pitfalls

**Sign errors**are common when expanding brackets. Pay attention to negatives.- Missing terms can occur during the `FOIL' step for new learners.
- Mistakes can happen with
**squared terms**, remember (x + a)² ≠ x² + a². - Take care with the order of operations to
**avoid miscalculations**.

Key Takeaways

- Mastering expanding brackets provides a
**foundation for more complex topics**in A-Level Mathematics. - Remember key identities such as the square of a binomial and difference of squares.
- Always
**check your work**for possible sign errors to ensure accuracy.