Algebra
№ 84Sheet № 84 · Foundation + Higher · AQA · Edexcel · OCR
Expanding Double Brackets –
Expanding double brackets is a fundamental algebra skill tested on both Foundation and Higher tier GCSE Maths papers. You will need it for factorising quadratics, solving equations, and graph work, so it is worth practising until the method is automatic.
§Key definitions
Question:
Expand and simplify (x + 4)(x + 6).
Answer:
x² + 10x + 24
Q1 (Foundation):
Expand and simplify (x + 5)(x + 2).
Q2 (Foundation):
Expand and simplify (x - 3)(x + 8).
Q3 (Higher):
Expand and simplify (4x + 1)(2x - 3).
§Formulas to memorise
(x + a)(x + b) = x² + (a + b)x + ab
(a + b)(a - b) = a² - b²
Worked example
Expand and simplify (x + 4)(x + 6).
Working:
⚠ Common mistakes
- ✗Forgetting the inner or outer product. Students sometimes write only three terms instead of four. Using FOIL labels or a grid prevents this.
- ✗Sign errors with negatives. In (x - 3)(x + 5), the inner product is -3 times x = -3x, not +3x. Track signs carefully at every multiplication.
- ✗Writing (x + 4)² as x² + 16. You must expand as (x + 4)(x + 4) = x² + 8x + 16. The middle term 2ab is always present when the bracket is squared.
✦ Exam tips
- →If the question says "expand and simplify," you must collect like terms or you will lose a mark.
- →Use the grid method if you keep making errors with FOIL — it lays out all four products visually.
- →Check your expansion by substituting x = 1 into both the brackets and the expanded form; the two results should match.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/expanding-double-brackets