MathematicsExam code: 0580
Expanding and Factorising Brackets
Algebra and Sequences
Multiplying through
- Expanding removes a bracket by multiplying the outside term by every term inside it
- Each product keeps the sign that belongs to its term
- 5a(2a − 7) gives 10a² − 35a
- A negative outside the bracket changes the sign of every term inside
- −3y(2y − 4) gives −6y² + 12y
- Writing the negative term in brackets while multiplying keeps the sign rules visible
Worked example
Expanding a single bracket
Expand 4x(3x − 5).
Solution:
- Expanding removes the bracket by multiplying the term outside it by every term inside
- The bracket holds two terms, so there are two products to write
- Take each inside term with the sign in front of it: +3x and −5
- 4x × 3x = 12x², because 4 × 3 = 12 and x × x = x²
- 4x × (−5) = −20x, negative because one factor is negative
- The answer is 12x² − 20x
- The two terms are unlike, one in x² and one in x, so nothing collects and this is the simplest form
- Check with a value: x = 2 gives 8 × 1 = 8 in the question, and 48 − 40 = 8 in the answer
- The minus sign belongs to the 5 and travels with it, which is where most sign errors in this topic start