Expanding double brackets
Writing two brackets next to each other means the brackets need to be multiplied together. For example, \((y + 2)(y + 3)\) means \((y + 2) \times (y + 3)\).
When expanding double brackets, every Terms are individual components of expressions or equations. For example, in the expression 7a + 4, 7a is a term as is 4. in the first bracket has to be multiplied by every term in the second bracket. It is helpful to always multiply the terms in order so none are forgotten. One common method used is FOIL: First, Outside, Inside, Last.
Example
Expand the brackets \((y + 2)(y + 3)\).
Multiply the first items in the brackets: \(y \times y = y^2\)
Multiply the terms that are on the outsides of the brackets: \(y \times 3 = 3y\)
Multiply the terms on the insides of the brackets: \(2 \times y = 2y\)
Multiply the last terms in the brackets: \(2 \times 3 = 6\)
This gives: \(y^2 + 3y + 2y + 6\)
Simplify the like terms \((3y + 2y)\) to give \(y^2 + 5y + 6\).
Question
Expand the bracket \((2m - 3)(m + 1)\).
- Firsts = \(2m \times m = 2m^2\)
- Outsides = \(2m \times 1 = 2m\)
- Insides = \(-3 \times m = -3m\)
- Lasts = \(-3 \times 1 = -3\)
This gives: \(2m^2 + 2m - 3m - 3\).
\(2m\) and \(-3m\) are like terms, as they both contain the letter \(m\).
\(2m - 3m = -1m\) which can be written as \(-m\).
Simplifying like terms gives: \(2m^2 - m - 3\).
Another method for multiplying brackets is to use a grid.
To expand the bracket \((2m - 3)(m + 1)\) :
So, \((2m - 3)(m + 1) = 2m^2 - 3m + 2m - 3 = 2m^2 - m - 3\).
More guides on this topic
- Algebraic formulae - Edexcel
- Solving linear equations - Edexcel
- Solving simultaneous equations - Edexcel
- Solving quadratic equations - Edexcel
- Algebraic fractions - Edexcel
- Inequalities - Edexcel
- Sequences - Edexcel
- Straight line graphs - Edexcel
- Other graphs - Edexcel
- Transformation of curves - Higher - Edexcel
- Using and interpreting graphs - Edexcel