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Factorization using Special Algebraic Identities

Factorization using Special Algebraic Identities
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2017-02-21 09:25
FunctionGeometric Construction
This example demonstrates how to use GeoGebra for factorizing special algebraic identities like perfect squares and difference of squares. Core math concepts include factorization, perfect square formula, difference of squares formula, and quadratic equations. GeoGebra commands used are RandomElement, Simplify, Factor, If, GCD, Segment, Midpoint, Polygon, and Coefficients. Suitable for high school mathematics education, enhancing understanding and application of algebraic identities.

GeoGebra Commands & Parameters

  1. RandomElement(list1) → b
  2. RandomElement(lista) → a
  3. Simplify((f1(x) * f2(x))) → f
  4. Simplify((f1(x))^(2)) → g
  5. Factor(g) → h
  6. Factor(f) → p
  7. RandomElement({2, 1, 2}) → show
  8. If(show ≟ 1, text1, text2) → textGeneratedExpression
  9. If(show ≟ 1, text5, text4) → text6
  10. GCD(a, b) → hcf
  11. Simplify(f1(x) / hcf) → f1g
  12. Simplify(f2(x) / hcf) → f2g
  13. Simplify((f1g(x))^(2)) → gg
  14. Factor(gg) → hg
  15. Simplify((f1g(x) * f2g(x))) → fg
  16. Factor(fg) → pg
  17. Segment(S_1, S_2) → c
  18. Segment(S_2, S_3) → d
  19. Segment(S_3, S_4) → e
  20. Segment(S_4, S_1) → i
  21. Midpoint(c) → C
  22. Midpoint(d) → D
  23. Midpoint(e) → E
  24. Midpoint(i) → F
  25. Segment(C, E) → j
  26. Segment(D, F) → k
  27. Midpoint(S_1, C) → G
  28. Midpoint(S_1, S_3) → H
  29. Midpoint(S_1, H) → I
  30. Midpoint(C, S_2) → J
  31. Midpoint(C, D) → K
  32. Midpoint(S_2, D) → L
  33. Midpoint(D, S_3) → M
  34. Midpoint(H, S_3) → N
  35. Midpoint(S_3, E) → O
  36. Midpoint(E, S_4) → P
  37. Midpoint(F, E) → Q
  38. Midpoint(F, S_4) → R
  39. Midpoint(F, S_1) → S
  40. Polygon(F, H, E, S_4) → poly1, f_1, h_1, e_1, s_4
  41. Polygon(C, S_2, D, H) → poly2, c_1, s_2, d_1, h_2
  42. Polygon(H, D, S_3, E) → poly3, h_3, d_2, s_3, e_2
  43. Polygon(S_1, C, H, F) → poly4, s_1, c_2, h_4, f_2
  44. Coefficients(g) → l1
  45. GCD(l1) → m