Expanding and Factorising

Expanding brackets and factorising are reverse operations — two of the most important algebraic skills in GCSE Mathematics. This lesson covers single brackets, double brackets, the difference of two squares, and factorising quadratics including those where a ≠ 1 (Higher tier).

---

Key Vocabulary

Term	Meaning
Expand	Multiply out the brackets
Factorise	Write as a product of factors (put back into brackets)
Common factor	A factor shared by every term
Quadratic expression	An expression of the form ax² + bx + c
Difference of two squares	An expression of the form a² − b²

---

Expanding Single Brackets

Multiply the term outside the bracket by every term inside.

Worked Example 1

Expand: 3(2x + 5)

= 3 × 2x + 3 × 5 = 6x + 15

Worked Example 2

Expand: −2x(3x − 4y + 1)

= (−2x)(3x) + (−2x)(−4y) + (−2x)(1)

= −6x² + 8xy − 2x

Answer: −6x² + 8xy − 2x

---

Expanding Double Brackets