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A-Level Revise Aid: This resource is designed to support your revision and may contain errors. If you find a discrepancy with your class teaching, your teacher is correct -- please let us know at alevelrevise@scott.scottrix.co.uk.

Algebraic Expressions

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

A-Level Mathematics revision: Algebraic Expressions. Learning objectives, key points, worked examples and practice questions across AQA, Edexcel, OCR, WJEC and CCEA.

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πŸ“Œ Key Points

Key Fact: Collecting like terms: only terms with identical variables and powers can be combined
Key Fact: Expanding brackets: multiply each term inside by the term outside (FOIL for double brackets)
Key Fact: Difference of two squares: a^2 - b^2 = (a + b)(a - b)
Key Fact: Perfect square trinomials: a^2 +/- 2ab + b^2 = (a +/- b)^2
Key Fact: Factorising by grouping: pair terms to extract common factors
Key Fact: Algebraic fractions: factorise numerator and denominator first, then cancel common factors
Key Fact: Index laws: xᡃ x xᡇ = xᡃ⁺ᡇ, xᡃ Γ· xᡇ = xᡃ⁻ᡇ, (xᡃ)ᡇ = xᡃᡇ, x⁰ = 1, x⁻ᡃ = 1/xᡃ
Key Fact: Polynomial long division: dividend = divisor x quotient + remainder
Key Fact: Factor theorem: if f(a) = 0 then (x - a) is a factor of f(x)

🎯 Learning Objectives

  • Simplify algebraic expressions by collecting like terms
  • Expand single and double brackets using distributive law
  • Factorise quadratic expressions including difference of two squares
  • Manipulate algebraic fractions with numerical and algebraic denominators
  • Apply index laws to simplify expressions with powers
  • Use the factor theorem and remainder theorem for polynomial division

πŸ’‘ Worked Example

Exam-Style Question

Question: Simplify fully: (2x^2 + 3x - 2)/(x + 2) - (x^2 - 4)/(x - 2)

Model Answer:

Factorise: (2x-1)(x+2)/(x+2) - (x-2)(x+2)/(x-2) = (2x-1) - (x+2) = x - 3

❓ Practice Questions

Questions:

  • Expand and simplify (3x - 2)(x + 4) - (x - 1)^2
  • Factorise completely: 6x^2 + 13x + 6
  • Simplify: (x^3 - 8)/(x^2 - 4)
  • Divide 2x^3 - 5x^2 + 3x - 1 by (x - 2) using polynomial division
  • Given f(x) = x^3 - 6x^2 + 11x - 6, show (x-1) is a factor and factorise fully
  • Simplify: (2x^2y⁻^3)^3 Γ· (4x⁻¹y^2)^2

🎬 Video Resources

πŸ“„ Past Papers & Exam Resources

πŸ”— Further Reading & Resources