Sheet № 11 · Foundation + Higher · AQA · Edexcel · OCR
Simplifying Expressions –
Simplifying expressions is one of the first algebra skills you meet at GCSE, and it appears on virtually every paper at both Foundation and Higher tier. Whether a question explicitly says "simplify" or whether simplification is just one step inside a larger problem, you need to collect like terms confidently and apply index laws correctly
§Key definitions
Example:
Simplify 4x + 3y − 2x + 5y − 1.
Question:
Simplify 6a + 4b − 3a + 2b − 5.
Answer:
3a + 6b − 5
Q1 (Foundation):
Simplify 5m − 2n + 3m + 7n.
Q2 (Foundation):
Simplify 2p × 5p³.
§Formulas to memorise
Like terms have identical variable parts: ax^n and bx^n are like terms and can be combined to give (a + b)x^n
When multiplying terms, multiply coefficients and add indices: ax^m × bx^n = abx^(m+n)
When dividing terms, divide coefficients and subtract indices: ax^m ÷ bx^n = (a/b)x^(m−n)
x terms: 4x − 2x = 2x
y terms: 3y + 5y = 8y
Coefficients: 3 × 4 = 12
a: a² × a = a³
b: b × b³ = b⁴
Cancel any variable whose power becomes zero (since x⁰ = 1).
Coefficients: 10 ÷ 2 = 5
x: x⁵ ÷ x² = x³
Example:: Simplify 4x + 3y − 2x + 5y − 1.
Worked example
Simplify 6a + 4b − 3a + 2b − 5.
Working:
⚠ Common mistakes
- ✗Combining unlike terms. 3x + 2x² cannot be simplified to 5x² or 5x³. The powers of x are different, so these are separate terms.
- ✗Forgetting the sign of a term. In 7 − 3x + 2x, some students miss that the 3x is negative and write 7 + 5x instead of the correct 7 − x.
- ✗Dropping variables when adding. 4x + 3x = 7x, NOT 7. The x does not disappear.
- ✗Confusing multiplication with addition. When multiplying x² × x³, add the powers to get x⁵. When adding x² + x³, you cannot combine them at all.
- ✗Not fully simplifying. If the question says "simplify fully", check that no further collecting or cancelling is possible. An answer of 6x + 2x − 3 should be written as 8x − 3.
✦ Exam tips
- →Underline or highlight like terms in different colours (on rough paper) to avoid missing any. This is a technique top students use to stay organised.
- →Write the sign in front of each term as part of that term. Treat 5x − 3y + 2x as (+5x), (−3y), (+2x). This reduces sign errors.
- →When a question combines simplifying with expanding brackets, expand first, then collect like terms. Multi-step problems often require both skills together.