VISUALISATIONS OF ALGEBRAIC PROCESSES AND STRUCTURES

Vladimir Miškovic

• ACKNOWLEDGEMENTS
• INTRODUCTION
• VISUAL ALGEBRA I: Algebraic Expansions
  • Introduction
  • Binomial Expansions
  • Generalisation of Binomial Expansions
  • Expansions and Simplifications
  • Trinomial Expansions
  • Generalisation of Trinomial Expansions
  • Two-Stage Expansions
  • Quadrtatic Expansions
  • Two-Step Two-Stage Expansions
  • Two-Step Two-Stage Quadratic Expansions
  • Examples of Quadratic Expansions
  • Comparison of Differences
  • Multiplication of Polynomials
  • Cubic Expansions
  • Index
• VISUAL ALGEBRA II: Algebraic Factorisations
  • Introduction
  • One Stage Factorisations
  • Two-Stage Factorisations
  • Factorisations of Quadratics with Rational Coefficients and Real Factors
  • Applications of Rational Quadratic Factorisations and Expansions
  • Two-Step Two-Stage Factorisations with a Common Factor
  • Two-Step Two-Stage Quadratic Factorisations with a Common Factor
  • Examples of Two-Step Two-Stage Quadratic Factorisations with a Common Factor
  • Two-Step Two-Stage Quadratic Factorisations without a Common Factor
  • Three-Step Quadratic Factorisations
  • Index
• VISUAL ALGEBRA III: Factorisation of Polynomials and Extension Materials
  • Introduction
  • Quadratics with Real Coefficients and Factorised with Conjugate Complex Factors
  • Quadratics with an Imaginary Linear Term and Factorised with Both Complex Factors
  • Quadratics with a Complex Linear and an Imaginary Constant Term and Factorised with a Combination of Rational and Complex Factors
  • Factorisations of Other Types of Complex Quadratics
  • Factorisations of Rational Polynomials
  • Factorisations of Polynomials with Complex Factors
  • Extension Exercises
  • Index
• INSTEAD OF CONCLUSION