# Expanding Brackets

## Expanding Brackets

**H1 Expanding Single Brackets**

- A term outside of the bracket must be multiplied by
**each term inside**of the bracket - Apply the
**distributive law**:**a(b + c) = ab + ac** - For example, expand 3(x + 2), 3 multiplied by x is 3x, and 3 multiplied by 2 is 6, so it expands to 3x + 6

**H1 Expanding Double Brackets**

- When expanding double brackets, remember the method:
**first, outside, inside, last (FOIL)** - First apply the
**FOIL method**: expand (a + x)(b + y) to get ab + ay + bx + xy - For example, expand (x + 2)(x - 3), first: x
*x = x^2, outside: x*(-3) = -3x, inside: 2*x= 2x, last: 2*(-3)= -6. Final Result: x^2 - 3x + 2x - 6 = x^2 - x - 6

**H1 Special Cases in Expanding Brackets**

- Recognize perfect squares: Implement the rule
**(x + a)^2 = x^2 + 2ax + a^2** - For example, (x + 3)^2 = x^2 + 6x + 9
- Pay special attention to
**difference of two squares**:**(a + b)(a - b) = a^2 - b^2** - For example, with (x + 6)(x - 6), the answer will be x^2 - 36