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Distributive Property Demo

Distributive Property Demo
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2019-01-16 23:19
FunctionCalculusGeometric Construction
This example demonstrates the geometric intuition and algebraic verification of the distributive property for polynomials; involves core concepts like distributive property, polynomial expansion, and random polynomial generation; constructed using commands like If, Random, Polynomial, Expand, LaTeX, and objects such as monomial1, poly1, expand; suitable for high school mathematics teaching to understand the geometric meaning of algebraic operations and randomness.

GeoGebra Commands & Parameters

  1. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[2, 5]) → monomial1
  2. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[2, 5]) → monomial2
  3. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[1, 5]) → poly1coeff1
  4. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[1, 5]) → poly1coeff3
  5. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[1, 5]) → poly1coeff4
  6. Random(-5, 5) → poly2coeff1
  7. Random(-5, 5) → poly1coeff2
  8. Polynomial((poly1coeff1 * x^(3)) + (poly1coeff2 * x^(2)) + (poly1coeff3 * x) + poly1coeff4) → poly1
  9. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[1, 5]) → poly2coeff2
  10. Random(-5, 5) → poly2coeff3
  11. If(Random[0, 1] ≟ 0, Random[-5, -1], Random[1, 5]) → poly2coeff4
  12. Polynomial((poly2coeff1 * x^(3)) + (poly2coeff2 * x^(2)) + (poly2coeff3 * x) + poly2coeff4) → poly2
  13. Expand(sum) → correctAnswer
  14. Polynomial((x3coeff * x^(3)) + (x2coeff * x^(2)) + (x1coeff * x) + x0coeff) → userAnswer
  15. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  16. LaTeX(sum) → expression
  17. LaTeX(Expand[monPoly1] + Expand[monPoly2]) → distribute
  18. LaTeX((x0coeff * "\vphantom{x^3}")) → x0Label
  19. LaTeX((x1coeff * "x\vphantom{x^3}")) → x1Label
  20. LaTeX((x2coeff * "x^2")) → x2Label
  21. LaTeX((x3coeff * "x^3")) → x3Label