An Exercise on Three Core Factorization Techniques: Common Factor + Formulas + Grouping

Published: 2026-08-04 Categories: Equations and Identities Editor: MathSir Difficulty: ★★★☆☆ Reading time: ~14 minutes Pageview: 35

Synopsis

Factorization is the bedrock of DSE algebra. This article covers the three essential techniques every candidate must master: taking out the common factor, applying algebraic identities (difference of squares, perfect squares, sum/difference of cubes), and grouping. You will learn how to recognise which method to use, avoid common traps, and apply these skills to DSE-style Section A(1) and A(2) questions. Complete with worked examples, exam tips, and 10 practice questions.

Article

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 Three Core Factorization Techniques: Common Factor + Formulas + Grouping

Exercise

Factorise each expression completely.

  1. \(8x^2y - 12xy^2\)
  2. \(a^2 - 49\)
  3. \(4x^2 + 12x + 9\)
  4. \(27x^3 + 8\)
  5. \(xy - 2x + 3y - 6\)
  6. \(6x^3 - 9x^2 + 2x - 3\)
  7. \(16x^4 - 81\)
  8. \(x^3 - 3x^2 - 4x + 12\)
  9. \(2x^4 - 32\)
  10. \(x^4 - 10x^2 + 9\) A(2)-style

Answer Key

1. \(4xy(2x - 3y)\)
2. \((a - 7)(a + 7)\)
3. \((2x + 3)^2\)
4. \((3x + 2)(9x^2 - 6x + 4)\)
5. \((y - 2)(x + 3)\)
6. \((2x - 3)(3x^2 + 1)\)
7. \((4x^2 - 9)(4x^2 + 9) = (2x - 3)(2x + 3)(4x^2 + 9)\)
8. \((x - 3)(x - 2)(x + 2)\)
9. \(2(x^4 - 16) = 2(x^2 - 4)(x^2 + 4) = 2(x - 2)(x + 2)(x^2 + 4)\)
  
10. \((x^2 - 1)(x^2 - 9) = (x - 1)(x + 1)(x - 3)(x + 3)\)

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