Multiplying Double Brackets – GCSE Mathematics (Foundation) AQA Revision

Definition of Multiplying Double Brackets

Multiplying double brackets is a core concept in algebra.
It refers to the process of expanding and simplifying an equation or expression where two brackets are multiplied together.
Each term in one bracket needs to be multiplied by each term in the other bracket.

FOIL is a mnemonic to remember the process of multiplying double brackets: First, Outer, Inner, Last.
First represents the product of the first terms in each bracket.
Outer represents the product of the outer terms in the brackets.
Inner represents the product of the inner terms in the brackets.
Last represents the product of the last terms in each bracket.

To multiply double brackets, apply the FOIL method.
Example: Expand and simplify the expression (2x + 3)(x - 1).
First: Multiply the first terms in each bracket: 2x * x = 2x^2.
Outer- Multiply the outer terms in the brackets: 2x * (-1) = -2x.
Inner- Multiply the inner terms in the brackets: 3 * x = 3x.
Last: Multiply the last terms in each bracket: 3 * (-1) = -3.
Add these expressions together to simplify: 2x^2 - 2x + 3x - 3 = 2x^2 + x - 3. This is the expanded and simplified expression.

Mistaking the order of FOIL: It is crucial to follow the exact order - first, outer, inner, last.
Forgetting to multiply every term in each bracket with each other.
Neglecting to simplify: Always ensure to combine like terms after multiplying the brackets.