DfE statement A4 · Algebra
Simplifying, expanding and factorising
Simplifying, expanding and factorising is content statement A4 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + bx + c; simplifying expressions involving sums, products and powers, including the laws of indices." (statement A4). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "algebraic fractions", "or more", "factorising quadratic expressions of the form ax² + bx + c". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- (a + b)² = a² + b². Squaring a bracket means multiplying it by itself, which gives a² + 2ab + b².
- Multiplying only the first terms of two brackets and the last terms, missing the two cross products.
- Factorising incompletely: writing 6x + 12 as 2(3x + 6) or 3(2x + 4) when 6(x + 2) is required, or leaving a common letter behind.
- Factorising x² − 9 as (x − 3)². The difference of two squares is (x + 3)(x − 3).
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is simplifying, expanding and factorising on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "algebraic fractions", "or more", "factorising quadratic expressions of the form ax² + bx + c" — are Higher only; the rest is Foundation content.
Can I use a calculator for simplifying, expanding and factorising?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
How do I factorise x² + bx + c?
Find two numbers that multiply to c and add to b, then write the brackets with those numbers. For x² + 7x + 12 the numbers are 3 and 4, giving (x + 3)(x + 4). If c is negative, the two numbers have opposite signs. Factorising ax² + bx + c, where a is not 1, is Higher tier.
What is the single most common mistake here?
(a + b)² = a² + b². Squaring a bracket means multiplying it by itself, which gives a² + 2ab + b².
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Algebra at Foundation or at Higher.