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Algebra Practice: Applying Three Binomial Formulas

Algebra Practice: Applying Three Binomial Formulas
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2024-07-01 17:17
Sequence
In collections Binomische Formeln
This example demonstrates the derivation, graphical representation, and application of three binomial formulas. Key mathematical concepts include three binomial formulas, algebraic expressions, and practice. GeoGebra commands such as Element, Join, and Sort are used in construction. Suitable for 7-8 grade students for learning and practice.

GeoGebra Commands & Parameters

  1. Element(Auswahl, questionCount) → randomQuestion
  2. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order01
  3. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(3\:a \cdot 4\:b \cdot 4\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:a + 4\:b\right) \cdot 2\)\vphantom{gb²}}$", "$\textsf{\(3\:a + 4\:b\)\vphantom{gb²}}$", "$\textsf{\(9\:a² + 24\:a\:b + 16\:b²\)\vphantom{gb²}}$"}, Order01) → dropdown01
  4. Join({Set1, Set2, Set3}) → Set123
  5. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order02
  6. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(25\:c² + 20\:a\:c + 4\:a²\)\vphantom{gb²}}$", "$\textsf{\(2 \cdot 5\:c + 2 \cdot 2\:a\)\vphantom{gb²}}$", "$\textsf{\(25\:c² - 20\:a\:c + 4\:a²\)\vphantom{gb²}}$", "$\textsf{\(25\:c² + 4\:a²\)\vphantom{gb²}}$"}, Order02) → dropdown02
  7. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order03
  8. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(4\:k² + 40\:k\:n + 100\:n²\)\vphantom{gb²}}$", "$\textsf{\(\left(2\:k\right)² + \left(10\:n\right)²\)\vphantom{gb²}}$", "$\textsf{\(2 \cdot 2\:k \cdot 10\:n\)\vphantom{gb²}}$", "$\textsf{\(2\:k \cdot 10\:n\)\vphantom{gb²}}$"}, Order03) → dropdown03
  9. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order04
  10. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(64\:g² - 48\:g\:f + 9\:f²\)\vphantom{gb²}}$", "$\textsf{\(64\:g² + 48\:g\:f + 9\:f²\)\vphantom{gb²}}$", "$\textsf{\(\left(8\:g + 3\:f\right)²\)\vphantom{gb²}}$", "$\textsf{\(8\:g²\)\vphantom{gb²}}$"}, Order04) → dropdown04
  11. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order05
  12. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(49\:y² - 28\:x\:y + 4\:x²\)\vphantom{gb²}}$", "$\textsf{\(\left(7\:y\right)² - \left(2\:x\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(7\:y + 2\:x\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(2\:x\right)² - \left(7\:y\right)²\)\vphantom{gb²}}$"}, Order05) → dropdown05
  13. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order06
  14. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(100\:u²\)\vphantom{gb²}}$", "$\textsf{\(10\:u - 3\:v\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:u + 3\:v\right)²\)\vphantom{gb²}}$", "$\textsf{\(100\:u² - 60\:u\:v + 9\:v²\)\vphantom{gb²}}$"}, Order06) → dropdown06
  15. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order07
  16. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(4\:k + 2\:l\right) \cdot \left(4\:k - 2\:l\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k + 2\:l\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k\right)² + \left(2\:l\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k - 2\:l\right)²\)\vphantom{gb²}}$"}, Order07) → dropdown07
  17. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order08
  18. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(3\:b + 4\:c\right) \cdot \left(3\:b + 4\:c\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:b + 4\:c\right)\:(3\:b - 4\:c)\)\vphantom{gb²}}$", "$\textsf{\(3\:b² + 4\:c \cdot \left(3\:b - 4\:c\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:b - 4\:c\right)²\)\vphantom{gb²}}$"}, Order08) → dropdown08
  19. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order09
  20. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(10\:r + 2\:s\right)²\)\vphantom{gb²}}$", "$\textsf{\(100\:r² + 2 \cdot 10\:r \cdot 2\:s - 4\:s²\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:r - 2\:s\right)\:\left(10\:r + 2\:s\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:r - 2\:s\right)²\)\vphantom{gb²}}$"}, Order09) → dropdown09
  21. If(randomQuestion ≟ 1, SelectedIndex[dropdown01], randomQuestion ≟ 6, SelectedIndex[dropdown06], randomQuestion ≟ 7, SelectedIndex[dropdown07], randomQuestion ≟ 8, SelectedIndex[dropdown08], SelectedIndex[dropdown09], randomQuestion ≟ 2, SelectedIndex[dropdown02], randomQuestion ≟ 3, SelectedIndex[dropdown03], randomQuestion ≟ 4, SelectedIndex[dropdown04], randomQuestion ≟ 5, SelectedIndex[dropdown05]) → actualIndex123
  22. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order10
  23. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(14 + 3,6\right)²\)\vphantom{gb²}}$", "$\textsf{\(3,6² + 14²\)\vphantom{gb²}}$", "$\textsf{\(3,6 + 14\)\vphantom{gb²}}$", "$\textsf{\(14 \cdot 3,6\)\vphantom{gb²}}$"}, Order10) → dropdown10
  24. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order11
  25. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(30 - 12\right)²\)\vphantom{gb²}}$", "$\textsf{\(30² - 12²\)\vphantom{gb²}}$", "$\textsf{\(30² - 60 \cdot 12 + 12²\)\vphantom{gb²}}$", "$\textsf{\(30² - 12\)\vphantom{gb²}}$"}, Order11) → dropdown11
  26. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order12
  27. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(22² - 3²\)\vphantom{gb²}}$", "$\textsf{\(19² + 3²\)\vphantom{gb²}}$", "$\textsf{\(\left(22 + 3\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(22 - 3\right)²\)\vphantom{gb²}}$"}, Order12) → dropdown12
  28. If(randomQuestion ≟ 10, SelectedIndex[dropdown10], randomQuestion ≟ 11, SelectedIndex[dropdown11], SelectedIndex[dropdown12]) → actualIndex4
  29. Textfield(InputFunc) → InputBoxFunc
  30. If(randomQuestion ≟ 23, (5.22, 1.8), (5.22, 1.98)) → PosA2
  31. Sequence(PosA2 + (k * Vector[PosA2, PosC2] / 8), k, 1, 7) → PosE22List
  32. Point(PosE22List) → PosE22
  33. Sequence(PosA2 + (k * Vector[PosA2, PosC2] / 10), k, 6, 13) → PosE23List
  34. Point(PosE23List) → PosE23
  35. If(randomQuestion ∈ Set123, actualIndex123 ≟ CorrectIndex123(randomQuestion), false, randomQuestion ∈ Set4, actualIndex4 ≟ CorrectIndex4(IndexOf[randomQuestion, Set4]), randomQuestion ∈ Set5, correctValue ∧ correctFactored ∧ correctNoSquare, randomQuestion ≟ 22, IndexOf[PosE22, PosE22List] ≟ 6, randomQuestion ≟ 23, IndexOf[PosE23, PosE23List] ≟ 5) → correct
  36. Element(randomQuestions, questionCount) → actualQuestion
  37. If(correctCount ≥ 5, (6.38, 2.6), (5, 2.6)) → PosBtnStartAgain
  38. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg041
  39. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg051
  40. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg061
  41. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg062
  42. Segment(PosD + (0, dis), PosC + (0, dis)) → seg091
  43. Segment((x(PosA), y(PosE3)) + ((-dis), 0), PosD + ((-dis), 0)) → seg092
  44. Segment(PosA2 - ((2 * dis), 0), (x(PosA2), y(PosE23)) - ((2 * dis), 0)) → seg231
  45. Segment(PosA2 - (0, (2 * dis)), (x(PosE23), y(PosA2)) - (0, (2 * dis))) → seg232
  46. If(randomQuestion ∈ Set123, actualIndex123 ≠ 1, true, randomQuestion ∈ Set4, actualIndex4 ≠ 1, randomQuestion ∈ Set5, Defined[InputFunc] ∧ (¬Defined[IndexOf[",", Text[InputBoxFunc]]]), randomQuestion ≟ 22, movedE22, randomQuestion ≟ 23, movedE23) → clickableBtnValidate
  47. Element({600, 600, 625, 600, 550, 610, 610, 610, 650}, randomQuestion) → FBSet123PixX
  48. Segment(PosASol2 + (0, -0.2), PosASol2 + ((dim * sideLength2), -0.2)) → segSol231
  49. If(randomQuestion ≟ 22, PosE22, PosE23) → ArrowCenter
  50. Rotate(Segment[ArrowCenter + (arrowDistance, 0), ArrowCenter + (arrowDistance + arrowLength, 0)], arrowAngle + ((1 - 1) * (360°) / arrowNumber), ArrowCenter) → arrow1
  51. Rotate(Segment[ArrowCenter + (arrowDistance, 0), ArrowCenter + (arrowDistance + arrowLength, 0)], arrowAngle + ((2 - 1) * (360°) / arrowNumber), ArrowCenter) → arrow2
  52. If(randomQuestion ≟ 22, ¬movedE22, randomQuestion ≟ 23, ¬movedE23, false) → showArrows
  53. PolyLine(PosSB, Corner[txtStart, 1] + (0.5, -0.05), Corner[txtStart, 2] + (0.05, -0.05), Corner[txtStart, 3] + (0.05, 0.1), Corner[txtStart, 4] + (-0.05, 0.1), Corner[txtStart, 1] + (-0.05, 0.5), PosSB) → sb00
  54. PolyLine(PosSB, Corner[txtQuestionSet1, 1] + (-0.05 + 0.5, 0.1), Corner[txtQuestionSet1, 2] + (0.05, 0.1), Corner[txtQuestionSet1, 3] + (0.05, 0.1), Corner[txtQuestionSet1, 4] + (-0.05, 0.1), Corner[txtQuestionSet1, 1] + (-0.05, 0.5), PosSB) → sb01
  55. PolyLine(PosSB, Corner[txtQuestion10, 1] + (-0.05, 0.5), Corner[txtQuestion10, 1] + (-0.05, 0.1), Corner[txtQuestion10, 2] + (0.05, 0.1), Corner[txtQuestion10, 3] + (0.05, 0.1), Corner[txtQuestion10, 4] + (-0.05, 0.1), Corner[txtQuestion10, 1] + (-0.05, 1), PosSB) → sb10
  56. PolyLine(PosSB, Corner[txtQuestion11, 1] + (-0.05, 0.5), Corner[txtQuestion11, 1] + (-0.05, 0.1), Corner[txtQuestion11, 2] + (0.05, 0.1), Corner[txtQuestion11, 3] + (0.05, 0.1), Corner[txtQuestion11, 4] + (-0.05, 0.1), Corner[txtQuestion11, 1] + (-0.05, 1), PosSB) → sb11
  57. PolyLine(PosSB, Corner[txtQuestion12, 1] + (-0.05, 2.5), Corner[txtQuestion12, 1] + (-0.05, 0.1), Corner[txtQuestion12, 2] + (0.05, 0.1), Corner[txtQuestion12, 3] + (0.05, 0.1), Corner[txtQuestion12, 4] + (-0.05, 0.1), Corner[txtQuestion12, 1] + (-0.05, 3), PosSB) → sb12
  58. PolyLine(PosSB, Corner[txtQuestionSet5, 1] + (-0.05 + 0.5, 0.1), Corner[txtQuestionSet5, 2] + (0.05, 0.1), Corner[txtQuestionSet5, 3] + (0.05, 0.1), Corner[txtQuestionSet5, 4] + (-0.05, 0.1), Corner[txtQuestionSet5, 1] + (-0.05, 0.5), PosSB) → sb13
  59. PolyLine(PosSB, Corner[txtQuestion22, 1] + (-0.05, 1.25), Corner[txtQuestion22, 1] + (-0.05, 0.1), Corner[txtQuestion22, 2] + (0.05, 0.1), Corner[txtQuestion22, 3] + (0.05, 0.1), Corner[txtQuestion22, 4] + (-0.05, 0.1), Corner[txtQuestion22, 1] + (-0.05, 1.75), PosSB) → sb22
  60. PolyLine(PosSB, Corner[txtQuestion23, 1] + (-0.05, 1.25), Corner[txtQuestion23, 1] + (-0.05, 0.1), Corner[txtQuestion23, 2] + (0.05, 0.1), Corner[txtQuestion23, 3] + (0.05, 0.1), Corner[txtQuestion23, 4] + (-0.05, 0.1), Corner[txtQuestion23, 1] + (-0.05, 1.75), PosSB) → sb23
  61. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg023
  62. Segment(PosD + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg024
  63. Segment(PosC + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg031
  64. Segment(PosD + ((-dis), 0), (x(PosA), y(PosE3)) + ((-dis), 0)) → seg071
  65. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE3)) + ((-dis), 0)) → seg072
  66. Segment(PosD + (0, dis), (x(PosE3), y(PosD)) + (0, dis)) → seg073
  67. Segment(PosC + (0, dis), (x(PosE3 + y(PosE3 - PosA)), y(PosC)) + (0, dis)) → seg074
  68. Segment((x(PosA), y(PosE3)) + (0, (-dis)), PosE3 + (0, (-dis))) → seg081
  69. Segment((x(PosB), y(PosE3)) + (0, (-dis)), PosE3 + (0, (-dis))) → seg082
  70. Segment(PosC + (0, dis), PosC - (x(PosE3 - PosA), 0) + (0, dis)) → seg083
  71. Segment(PosD + (0, dis), PosC - (x(PosE3 - PosA), 0) + (0, dis)) → seg084
  72. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE3)) + ((-dis), 0)) → seg085
  73. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg011
  74. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE12)) + ((-dis), 0)) → seg012
  75. Segment(PosD + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg021
  76. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg022
  77. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg032
  78. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg042
  79. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg043
  80. If(randomQuestion ≟ 10, 14 / 17.6, randomQuestion ≟ 11, 12 / 30, 19 / 22) → parSkizze
  81. Segment(PosSkizze + (0, dimSkizze + dis), PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis)) → segSkizze101
  82. Segment(PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis), PosSkizze + (dimSkizze, dimSkizze + dis)) → segSkizze102
  83. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze103
  84. Segment(PosSkizze + ((-dis), 0), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze104
  85. Segment(PosSkizze + (0, dimSkizze + dis), PosSkizze + ((parSkizze * dimSkizze), dimSkizze + dis)) → segSkizze111
  86. Segment(PosSkizze + (0, dimSkizze + dis + 0.65), PosSkizze + (dimSkizze, dimSkizze + dis + 0.65)) → segSkizze112
  87. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze113
  88. Segment(PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis), PosSkizze + (dimSkizze, dimSkizze + dis)) → segSkizze121
  89. Segment(PosSkizze + (0, dimSkizze + dis + 0.65), PosSkizze + (dimSkizze, dimSkizze + dis + 0.65)) → segSkizze122
  90. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * parSkizze))) → segSkizze123
  91. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg052
  92. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg053
  93. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg063
  94. Segment((x(PosA), y(PosE3)) + ((-dis), 0), PosA + ((-dis), 0)) → seg093
  95. Text("\textsf{\bold{Zieh mich!}}", PosE22, false, true, -1, 1) → CapZiehMich22
  96. Text("\textsf{\bold{Zieh mich!}}", PosE23, false, true, -1, 1) → CapZiehMich23
  97. Segment(PosA2 + (x((5 * Vector[PosA2, PosC2] / 10)), 0) + (0, -0.15), (x(PosE23), y(PosA2)) + (0, -0.15)) → seg233
  98. Segment(PosA2 + (0, y((5 * Vector[PosA2, PosC2] / 10))) + (-0.15, 0), (x(PosA2), y(PosE23)) + (-0.15, 0)) → seg234
  99. Segment(PosASol2 + (0, ((dim * sideLength2) * 5 / 10)) + (-0.15, 0), PosASol2 + (0, ((dim * sideLength2) * 10 / 10)) + (-0.15, 0)) → segSol232
  100. Point(Line[PosImgFuchsHappy21, xAxis]) → PosImgFuchsHappy22
  101. Join({Random[2, 2, 12], Random[1, 1, 9], {2, 2}}) → AttemptCountStartList
  102. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg013
  103. Segment(PosC + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg014
  104. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg033
  105. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE12)) + ((-dis), 0)) → seg034

AI Drawing Prompt Reference

Create an algebra practice interface with multiple dropdown questions, each showing an algebraic expression with options for expanded or factored forms. Include a title at the top, an input box, and a validate button. The graphic area contains coordinate axes and line segments forming geometric illustrations to aid understanding. The layout is clean and suitable for student practice.
The prompt above was compiled from the original drawing commands and is for reference only.