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Binomial Multiplication Example

Binomial Multiplication Example
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2024-07-01 15:32
In collections Multiplikation von Binomen
This example demonstrates the geometric interpretation and calculation process of binomial multiplication, involving core math concepts like polynomial multiplication rules, algebraic expression simplification, and geometric transformations. It utilizes GeoGebra commands and objects such as Textfield, Shuffle, Text, TextToUnicode, Polygon, Element, Append, Remove, Corner, Point, Circle, Vector, Co

GeoGebra Commands & Parameters

  1. Textfield(bInput) → InputBox2
  2. Shuffle({1, 2, 3, 4, 5, 6, 7, 8, 9}) → ListExNumLeicht, {2, 6, 9, 3, 1, 5, 4, 7, 8}
  3. Shuffle({10, 11, 12, 13, 14, 15, 16, 17, 18}) → ListExNumMittel, {10, 14, 17, 13, 18, 11, 15, 16, 12}
  4. Shuffle({19, 20, 21, 22, 23, 24, 25, 26, 27}) → ListExNumSchwer, {25, 20, 24, 23, 19, 27, 22, 26, 21}
  5. Text(I) → IText
  6. TextToUnicode(IText) → ITextUnicode
  7. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  8. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {2, 0, 5, 5, 8, 3, 1, 7, 8, 10, 2, 7, 2, 4, 3, 2, 9, 4, 6, 5, 8, 4, 8, 4, 10, 2, 1, 9, 10, 6, 1, 2, 10, 0, 4, 10, 2, 5, 9, 7, 3, 9, 2, 10, 4, 7, 8, 2, 9, 7, 10, 0, 6, 10, 5, 8, 2, 2, 7, 3, 7, 6, 9, 5, 2, 8, 8, 9, 6, 6, 8, 9, 3, 10, 8, 7, 3, 6, 8, 10, 3, 2, 2, 5, 8, 2, 3, 8, 6, 0, 3, 3, 10, 6, 9, 6, 4, 4, 6, 6}
  9. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  10. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 3, 6, 6, 1, 0, 1, 7, 8, 2, 2, 6, 8, 4, 9, 6, 4, 3, 7, 1, 6, 4, 8, 3, 3, 2, 7, 2, 1, 0, 8, 8, 5, 2, 5, 4, 9, 4, 10, 10, 7, 6, 9, 5, 9, 10, 4, 2, 6, 5, 7, 9, 10, 1, 1, 10, 10, 4, 5, 2, 7, 2, 4, 0, 7, 3, 4, 0, 1, 8, 2, 4, 8, 1, 0, 4, 9, 6, 7, 6, 4, 8, 4, 9, 0, 9, 8, 5, 3, 3, 10, 1, 7, 2, 8, 2, 3, 9, 2, 4}
  11. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  12. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  13. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  14. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  15. Textfield(cInput) → InputBox3
  16. Corner(BildBlue, 1) → controlBlue
  17. Corner(BildGelb, 1) → controlGelb
  18. Corner(BildRosa, 1) → controlRosa
  19. Corner(BildGreen, 1) → controlGreen
  20. Point(line3) → P
  21. Circle(P, Q) → circ
  22. Textfield(inputAdd1) → Eingabefeld1
  23. Textfield(inputAdd2) → Eingabefeld2
  24. Polygon(PtopLeftCornerFeedback_{1} + (0.95, 0), PtopRightCornerFeedback_{1} + (-0.1, 0), PbottomRightCornerFeedback_{1} + (-0.1, 0), PbottomLeftCornerFeedback_{1} + (0.95, 0)) → rectangleCorrect_{1}, strecke4, strecke1, strecke2, strecke3
  25. Polygon(PtopLeftCornerFeedback_{2}, PtopRightCornerFeedback_{2}, PbottomRightCornerFeedback_{2}, PbottomLeftCornerFeedback_{2}) → rectangleCorrect_{2}, ptopleftcornerfeedback_{2}, ptoprightcornerfeedback_{2}, pbottomrightcornerfeedback_{2}, pbottomleftcornerfeedback_{2}
  26. Polygon(PtopLeftCornerFeedback_{3}, PtopRightCornerFeedback_{3}, PbottomRightCornerFeedback_{3}, PbottomLeftCornerFeedback_{3}) → rectangleCorrect_{3}, ptopleftcornerfeedback_{3}, ptoprightcornerfeedback_{3}, pbottomrightcornerfeedback_{3}, pbottomleftcornerfeedback_{3}
  27. Point(circSpecial) → B_2
  28. Point(circ2) → C_2
  29. Point(circ2) → D_2
  30. Point(circ3) → E_2
  31. Point(circ3) → F_2
  32. Point(circ4) → G_2
  33. Point(circ4) → H_2
  34. Point(circ5) → I_2
  35. Point(circ5) → J_2
  36. Point(circ6) → K_2
  37. Point(circ6) → L_2
  38. Point(circ7) → M_2
  39. Point(circ7) → N_2
  40. Point(circ8) → O_2
  41. Point(circ8) → P_2
  42. Point(circ9) → Q_2
  43. Point(circ9) → R_2
  44. Point(circ10) → S_2
  45. Vector(B_2, C_2) → vec7
  46. Vector(D_2, E_2) → vec8
  47. Vector(F_2, G_2) → vec9
  48. Vector(H_2, I_2) → vec1
  49. Vector(J_2, K_2) → vec2
  50. Vector(L_2, M_2) → vec3
  51. Vector(N_2, O_2) → vec4
  52. Vector(P_2, Q_2) → vec5
  53. Vector(R_2, S_2) → vec6
  54. CountIf(a ≟ true, a, bv) → correctProblems
  55. TextToUnicode(Text15) → BuchstabenAlleUnicode
  56. Intersection(BuchstabenAlleUnicode, ITextUnicode) → BuchstabenInputUnicode
  57. TextToUnicode(ListFunktionSol(exNum)) → SolTextUnicode
  58. Intersection(SolTextUnicode, BuchstabenAlleUnicode) → BuchstabenSolUnicode
  59. Defined(I) → fixedhelper
  60. Corner(currentEx, 3) → AnchorBinomMitte
  61. Corner(currentEx, 4) → W_2
  62. Corner(Text3, 3) → Z_2
  63. Line(C_3, xAxis) → f
  64. Textfield(I) → InputBox1
  65. Distance(AnchorBinom2, AnchorBinom3) → a
  66. TextToUnicode(Element[ListeVariablen(1), 1]) → l1
  67. If(blue, controlBlue, gelb, controlGelb, rosa, controlRosa, controlGreen) → controlMaster
  68. Text(Text16, controlMaster + (1.2, -0.1), false, true, -1, 0) → Text17
  69. CircumcircleArc(AnchorBinom1 + derring, AnchorBogerl13, AnchorBinom3) → bogerl1
  70. CircumcircleArc(AnchorBinom1 + derring, AnchorBogerl14, AnchorBinom4) → bogerl2
  71. CircumcircleArc(Mirror[AnchorBinom2 + derring, f], Mirror[AnchorBogerl24, f], Mirror[AnchorBinom4, f]) → bogerl4
  72. CircumcircleArc(Mirror[AnchorBinom2 + derring, f], Mirror[AnchorBogerl23, f], Mirror[AnchorBinom3, f]) → bogerl3
  73. If(questionCount ≟ 1, circSpecial, questionCount ≟ 6, circ6, questionCount ≟ 7, circ7, questionCount ≟ 8, circ8, questionCount ≟ 9, circ9, questionCount ≟ 10, circ10, questionCount ≟ 2, circ2, questionCount ≟ 3, circ3, questionCount ≟ 4, circ4, questionCount ≟ 5, circ5) → Golasso