MathPlotAI Logo MathPlotAI

Application of the Binomial Formula

Application of the Binomial Formula
Loading the math board and drawing, please wait…
2024-06-26 16:56
CalculusDerivative
In collections Binomische Formeln
This example demonstrates the application of the binomial formula, particularly the expansion of expressions. Students can try to expand different expressions, such as (c - d)², (2g - h)², and (m - 6n)². Additionally, students can attempt to derive the proof of the binomial formula and explain why it applies to the expansion of expressions. This example is suitable for advanced math students, particularly those studying algebra and geometry. Using GeoGebra, students can visually see the application of the binomial formula and explore and understand the concept interactively.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 10, 2, 7, 8, 6, 9, 9, 7, 7}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. PolyLine(PosSB, Corner[txt011, 2] + (-0.5, 0.1), Corner[txt011, 1] + (-0.1, 0.1), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 3] + (0, 0.1), Corner[txt011, 2] + (0, 0.5), PosSB) → sb01
  5. Textfield(input023) → InputBox023
  6. PolyLine(PosSB, Corner[txt021, 2] + (-0.5, 0.1), Corner[txt021, 1] + (-0.1, 0.1), Corner[txt021, 4] + (-0.1, 0.1), Corner[txt021, 3] + (0, 0.1), Corner[txt021, 2] + (0, 0.5), PosSB) → sb02
  7. Polygon((0.16, 7.389999999999999), (12.139999999999993, 7.389999999999999), (12.139999999999993, 3.389999999999999), (0.16, 3.389999999999999)) → polyLight2, r, s, t, a
  8. PointIn(polyLight2) → Light
  9. Circle(Light, radius) → CTaschenlampe1
  10. Circle(Light, radius) → CTaschenlampe2
  11. Circle(MPTaschenlampe, 2.5) → CTaschenlampe3
  12. Line(MPTaschenlampe, Light) → GTaschenlampe
  13. Intersect(CTaschenlampe3, GTaschenlampe, 2) → PosTL1
  14. Intersect(CTaschenlampe3, GTaschenlampe, 1) → PosTL2
  15. Rotate(PosTL2 + (0.2 * UnitOrthogonalVector[GTaschenlampe]), -67°, MPTaschenlampe) → PosImgTaschenlampe2
  16. Tangent(PosTL2, CTaschenlampe1) → tangent1, tangent2
  17. PolyLine(PosSB, Corner[txt051, 2] + (0, 0.5), Corner[txt051, 2] + (0, 0), Corner[txt051, 1] + (-0.1, 0), Corner[txt051, 4] + (-0.1, 0.1), Corner[txt051, 3] + (0, 0.1), Corner[txt051, 2] + (0, 1), PosSB) → sb05
  18. PolyLine(PosSB, Corner[txt102, 2] + (0, 0.25), Corner[txt102, 2] + (0, 0), Corner[txt102, 1] + (-0.1, 0), Corner[txt102, 4] + (-0.1, 0.1), Corner[txt102, 3] + (0, 0.1), Corner[txt102, 2] + (0, 0.5), PosSB) → sb10
  19. Midpoint(PosA, PosC) → MPQuadrat
  20. Segment(MPQuadrat + (0.45, 0.45), PosC) → Diagonale1
  21. Point(Diagonale1) → PosP
  22. Segment(PosA + (0, If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, (-disCap1), (-disCap2)]), PosB + (0, If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, (-disCap1), (-disCap2)])) → segCap111
  23. Segment(PosB + (If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, disCap1, disCap2 + 0.7], 0), PosC + (If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, disCap1, disCap2 + 0.7], 0)) → segCap112
  24. Text("\textsf{a}", Midpoint[segCap112], false, true, 1, 0) → Cap112
  25. Segment(PosA + (0, (-disCap1)), PosP1 + (0, (-disCap1))) → segCap121
  26. Segment(PosB + (0, (-disCap1)), PosP1 + (0, (-disCap1))) → segCap122
  27. Segment(PosB + (disCap1, 0), PosP2 + (disCap1, 0)) → segCap123
  28. Segment(PosC + (disCap1, 0), PosP2 + (disCap1, 0)) → segCap124
  29. Text("\textsf{a \(-\) b}", Midpoint[segCap123], false, true, 1, 0) → Cap123
  30. Text("\textsf{b}", Midpoint[segCap124], false, true, 1, 0) → Cap124
  31. Text("\textsf{a}", Midpoint[segCap111] + (0, 0.05), false, true, 0, -1) → Cap111
  32. Text("\textsf{a \(-\) b}", Midpoint[segCap121] + (0, 0.05), false, true, 0, -1) → Cap121
  33. Text("\textsf{b}", Midpoint[segCap122] + (0, 0.05), false, true, 0, -1) → Cap122
  34. Segment(PosP1, PosP1 + (sidelength + 4, 0)) → segR1
  35. Point(segR1) → PosR1
  36. Polygon(PosR1, PosR1 + (2.049999999999999, 0), PosR1 + (2.049999999999999, 0) + (0, sidelength), PosR1 + (0, sidelength)) → polyR1, f, g, h, b
  37. Segment(PosP4, PosP4 + (sidelength + 4, 0)) → segR2
  38. Point(segR2) → PosR2
  39. Polygon(PosR2, PosR2 + (sidelength, 0), PosR2 + PosC - PosP2 + (sidelength, 0), PosR2 + PosC - PosP2) → polyR2, posr2, i, j, k
  40. Polygon(PosDD1, PosDD1 + (-0.85, -0.35), PosDD1 + (0.85, -0.35), PosDD1 + (0.85, 0.35), PosDD1 + (-0.85, 0.35), PosDD1 + (-0.85, -0.35)) → polyDD1, posdd1, l, m, n, p, q
  41. Text("\textsf{(a \(-\) b)²}", PosDD1 + (0, 0.1), false, true, 0, 0) → txtDD1
  42. PolyLine(PosSB, Corner[txt191, 2] + (0, 1), Corner[txt191, 2] + (0, 0), Corner[txt191, 1] + (-0.1, 0), Corner[txt191, 4] + (-0.1, 0.1), Corner[txt191, 3] + (0, 0.1), Corner[txt191, 2] + (0, 1.75), PosSB) → sb19
  43. PolyLine(PosSB, Corner[txt201, 2] + (0, 0.75), Corner[txt201, 2] + (0, 0), Corner[txt201, 1] + (-0.1, 0), Corner[txt201, 4] + (-0.1, 0.1), Corner[txt201, 3] + (0, 0.1), Corner[txt201, 2] + (0, 1.5), PosSB) → sb20
  44. Text("\textsf{\colorbox{white}{a \cdot b}}", PosR1 + (0.5 * (PosB - PosP1)) + (0.5 * (PosP2 - PosB)), false, true, 0, 0) → CapR1
  45. Text("\textsf{\colorbox{white}{a \cdot b}}", PosR2 + (0.5 * (PosP1 - PosA)) + (0.5 * (PosC - PosP2)), false, true, 0, 0) → CapR2
  46. PolyLine(PosR2, PosR2 + PosP1 - PosA, PosR1) → PL20
  47. PolyLine(PosR3 + {(0, 0), PosP2 - PosP, PosC - PosP, PosP3 - PosP, (0, 0)}) → PLB4R
  48. PolyLine(PosSB + (0.15, -0.75), Corner[txt211, 2] + (0, 0.75), Corner[txt211, 2] + (0, 0), Corner[txt211, 1] + (-0.1, 0), Corner[txt211, 4] + (-0.1, 0.1), Corner[txt211, 3] + (0, 0.1), Corner[txt211, 2] + (0, 1.5), PosSB + (0.15, -0.75)) → sb21
  49. Textfield(input021) → InputBox021
  50. Textfield(input022) → InputBox022
  51. Sort({"$\textsf{\phantom{a²b²}\vphantom{+\(-\)b²}}$", "$\textsf{a²\phantom{b}\vphantom{+\(-\)b²}}$", "$\textsf{b²\phantom{b}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\)ab\phantom{²}\vphantom{+\(-\)b²}}$", "$\textsf{ba\phantom{²}\vphantom{+\(-\)b²}}$"}, OrderDD061) → dropdown061
  52. SelectedIndex(dropdown061) → index061
  53. Sort({"$\textsf{\phantom{a²b²}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) ab\phantom{²}\vphantom{+\(-\)b²}}$", "$\textsf{+ b²\phantom{b}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) a²\phantom{b²}\vphantom{+\(-\)b²}}$", "$\textsf{+ ab\phantom{²}\vphantom{+\(-\)b²}}$"}, OrderDD062) → dropdown062
  54. SelectedIndex(dropdown062) → index062
  55. Sort({"$\textsf{\phantom{a²b²}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) ba\phantom{²}\vphantom{+\(-\)b²}}$", "$\textsf{+ ab\phantom{²}\vphantom{+\(-\)b²}}$", "$\textsf{+ a²\phantom{b}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) b²\phantom{b}\vphantom{+\(-\)b²}}$"}, OrderDD063) → dropdown063
  56. SelectedIndex(dropdown063) → index063
  57. Sort({"$\textsf{\phantom{a²b²}\vphantom{+\(-\)b²}}$", "$\textsf{+ b²\phantom{a}\vphantom{+\(-\)b²}}$", "$\textsf{+ ab\phantom{²}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) b²\phantom{b}\vphantom{+\(-\)b²}}$", "$\textsf{\(-\) ba\phantom{²}\vphantom{+\(-\)b²}}$"}, OrderDD064) → dropdown064
  58. SelectedIndex(dropdown064) → index064
  59. PathParameter(PosP) → parP
  60. Join({{1}, Shuffle[2…5]}) → OrderDD161
  61. Sort({"$\textsf{\phantom{ a \(-\) b }\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{\(-\) }a\phantom{ b}\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{ \(-\) }b\phantom{ a}\vphantom{(b\(-\)a)}}$", "$\textsf{(a \(-\) b) \vphantom{(b\(-\)a)}}$", "$\textsf{(b \(-\) a) \vphantom{(b\(-\)a)}}$"}, OrderDD161) → dropdown161
  62. SelectedIndex(dropdown161) → index161
  63. Join({{1}, Shuffle[2…5]}) → OrderDD162
  64. Sort({"$\textsf{\phantom{ a \(-\) b }\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{\(-\) }a\phantom{ b}\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{ \(-\) }b\phantom{ a}\vphantom{(b\(-\)a)}}$", "$\textsf{(a \(-\) b) \vphantom{(b\(-\)a)}}$", "$\textsf{(b \(-\) a) \vphantom{(b\(-\)a)}}$"}, OrderDD162) → dropdown162
  65. SelectedIndex(dropdown162) → index162
  66. Join({{1}, Shuffle[2…5]}) → OrderDD191
  67. Sort({"$\textsf{\phantom{ a \(-\) b }\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{\(-\) }a\phantom{ b}\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{ \(-\) }b\phantom{ a}\vphantom{(b\(-\)a)}}$", "$\textsf{(a \(-\) b) \vphantom{(b\(-\)a)}}$", "$\textsf{(b \(-\) a) \vphantom{(b\(-\)a)}}$"}, OrderDD191) → dropdown191
  68. SelectedIndex(dropdown191) → index191
  69. Join({{1}, Shuffle[2…5]}) → OrderDD192
  70. Sort({"$\textsf{\phantom{ a \(-\) b }\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{\(-\) }a\phantom{ b}\vphantom{(b\(-\)a)}}$", "$\textsf{\phantom{ \(-\) }b\phantom{ a}\vphantom{(b\(-\)a)}}$", "$\textsf{(a \(-\) b) \vphantom{(b\(-\)a)}}$", "$\textsf{(b \(-\) a) \vphantom{(b\(-\)a)}}$"}, OrderDD192) → dropdown192
  71. SelectedIndex(dropdown192) → index192
  72. PointIn(polyLight2) → Light08
  73. Circle(Light08, radius) → CTaschenlampe081
  74. If(correct061 ∧ correct062 ∧ correct063, 4, correct061 ∧ correct062, 3, correct061, 2, 1) → step6
  75. CircleArc(Midpoint[PosCalc11, PosCalc14] + (0, dis6), PosCalc14, PosCalc11) → arc062
  76. CircleArc(Midpoint[PosCalc11, PosCalc13] + (0, dis6), PosCalc13, PosCalc11) → arc061
  77. If(IsInRegion[Corner[txtDD1, 1], Bereich1(1)] ∧ IsInRegion[Corner[txtDD1, 3], Bereich1(1)], 1, IsInRegion[Corner[txtDD1, 1], Bereich2(1)] ∧ IsInRegion[Corner[txtDD1, 3], Bereich2(1)], 2, IsInRegion[Corner[txtDD1, 1], Bereich3(1)] ∧ IsInRegion[Corner[txtDD1, 3], Bereich3(1)], 3, IsInRegion[Corner[txtDD1, 1], Bereich4(1)] ∧ IsInRegion[Corner[txtDD1, 3], Bereich4(1)], 4, NaN) → DragDrop14
  78. Circle(PointListMinus(2), radius) → sol031
  79. PolyLine(PosSB, Corner[txt041, 2] + (-0.5, 0.1), Corner[txt041, 1] + (-0.1, 0.1), Corner[txt041, 4] + (-0.1, 0.1), Corner[txt041, 3] + (0, 0.1), Corner[txt041, 2] + (0, 0.5), PosSB) → sb04
  80. PolyLine(PosSB, Corner[txt061, 2] + (-0.5, 0.1), Corner[txt061, 1] + (-0.1, 0.1), Corner[txt061, 4] + (-0.1, 0.1), Corner[txt061, 3] + (0, 0.1), Corner[txt061, 2] + (0, 0.5), PosSB) → sb06
  81. Mirror(CircleArc[Midpoint[PosCalc12, PosCalc13] + (0, dis6), PosCalc13, PosCalc12], SpiegelGerade) → arc063
  82. Mirror(CircleArc[Midpoint[PosCalc12, PosCalc14] + (0, dis6), PosCalc14, PosCalc12], SpiegelGerade) → arc064
  83. Text("\textsf{(a \(-\) b)²}", Midpoint[PosA, PosP] + (0, 0.1), false, true, 0, 0) → txt152
  84. Text("\textsf{\bold{Zieh mich!}}", PosP + (0.4, 0.3), false, true, 1, 0) → CapP12
  85. Segment(PosP + (-0.25, -0.25), PosP + (-0.75, -0.75)) → arrow12
  86. Textfield(input024) → InputBox024
  87. Textfield(input091) → InputBox091
  88. Text("\textsf{\bold{Zieh mich!}}", (11.5, 3.5) + (0, 1.25), false, true, 0, 0) → CapDD14
  89. Segment(Midpoint[Corner[CapDD14, 1], Corner[CapDD14, 2]], Midpoint[Corner[CapDD14, 1], Corner[CapDD14, 2]] + (0, -0.34)) → arrowDD14
  90. PolyLine(PosSB, Corner[txt071, 2] + (0, 0.25), Corner[txt071, 2] + (0, 0), Corner[txt071, 1] + (-0.1, 0), Corner[txt071, 4] + (-0.1, 0.1), Corner[txt071, 3] + (0, 0.1), Corner[txt071, 2] + (0, 0.75), PosSB) → sb07
  91. PolyLine(PosSB, Corner[txt031, 2] + (0, 0.25), Corner[txt031, 2] + (0, 0), Corner[txt031, 1] + (-0.1, 0), Corner[txt031, 4] + (-0.1, 0.1), Corner[txt031, 3] + (0, 0.1), Corner[txt031, 2] + (0, 0.75), PosSB) → sb03
  92. Circle(Light08, radius) → CTaschenlampe082
  93. Line(MPTaschenlampe, Light08) → GTaschenlampe08
  94. Intersect(CTaschenlampe3, GTaschenlampe08, 2) → PosTL081
  95. Intersect(CTaschenlampe3, GTaschenlampe08, 1) → PosTL082
  96. Rotate(PosTL082 + (0.2 * UnitOrthogonalVector[GTaschenlampe08]), -67°, MPTaschenlampe) → PosImgTaschenlampe082
  97. Tangent(PosTL082, CTaschenlampe081) → tangent081, tangent082
  98. Circle(PointList08(2) + (0.1, 0), radius) → sol081
  99. PolyLine(PosSB, Corner[txt082, 2] + (0, 0.25), Corner[txt082, 2] + (0, 0), Corner[txt082, 1] + (-0.1, 0), Corner[txt082, 4] + (-0.1, 0.1), Corner[txt082, 3] + (0, 0.1), Corner[txt082, 2] + (0, 0.75), PosSB) → sb08
  100. PolyLine(PosSB, Corner[txt092, 2] + (0, 0.25), Corner[txt092, 2] + (0, 0), Corner[txt092, 1] + (-0.1, 0), Corner[txt092, 4] + (-0.1, 0.1), Corner[txt092, 3] + (0, 0.1), Corner[txt092, 2] + (0, 0.75), PosSB) → sb09
  101. PolyLine(PosSB, Corner[txt112, 2] + (0, 0.25), Corner[txt112, 2] + (0, 0), Corner[txt112, 1] + (-0.1, 0), Corner[txt112, 4] + (-0.1, 0.1), Corner[txt112, 3] + (0, 0.1), Corner[txt112, 2] + (0, 0.75), PosSB) → sb11
  102. PolyLine(PosSB, Corner[txt121, 2] + (0, 0.25), Corner[txt121, 2] + (0, 0), Corner[txt121, 1] + (-0.1, 0), Corner[txt121, 4] + (-0.1, 0.1), Corner[txt121, 3] + (0, 0.1), Corner[txt121, 2] + (0, 0.75), PosSB) → sb12
  103. PolyLine(PosSB, Corner[txt131, 2] + (0, 0.25), Corner[txt131, 2] + (0, 0), Corner[txt131, 1] + (-0.1, 0), Corner[txt131, 4] + (-0.1, 0.1), Corner[txt131, 3] + (0, 0.1), Corner[txt131, 2] + (0, 0.75), PosSB) → sb13
  104. PolyLine(PosSB, Corner[txt141, 2] + (0, 0.25), Corner[txt141, 2] + (0, 0), Corner[txt141, 1] + (-0.1, 0), Corner[txt141, 4] + (-0.1, 0.1), Corner[txt141, 3] + (0, 0.1), Corner[txt141, 2] + (0, 0.75), PosSB) → sb14
  105. PolyLine(PosSB, Corner[txt151, 2] + (0, 0.25), Corner[txt151, 2] + (0, 0), Corner[txt151, 1] + (-0.1, 0), Corner[txt151, 4] + (-0.1, 0.1), Corner[txt151, 3] + (0, 0.1), Corner[txt151, 2] + (0, 0.75), PosSB) → sb15
  106. PolyLine(PosSB, Corner[txt161, 2] + (0, 0.75), Corner[txt161, 2] + (0, 0), Corner[txt161, 1] + (-0.1, 0), Corner[txt161, 4] + (-0.1, 0.1), Corner[txt161, 3] + (0, 0.1), Corner[txt161, 2] + (0, 1.25), PosSB) → sb16
  107. Sequence(PosQ4 + (k / 20 * (PosQ1 - PosQ4)), k, 0, 20) → PointsP11
  108. Point(PointsP11) → PosP11
  109. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\↓\end{array}}}", PosP11 + (-0.25, 0), false, true, 1, -1) → CapZiehMich11
  110. Segment(PosQ4 + (0, disQ1), PosQ34 + (0, disQ1)) → segQ111
  111. Segment(PosQ3 + (0, disQ1), PosQ34 + (0, disQ1)) → segQ112
  112. Segment(PosQ3 + (0, If[step ≟ 12, 0, 0.65] + disQ1), PosQ4 + (0, If[step ≟ 12, 0, 0.65] + disQ1)) → segQ113
  113. Segment(PosQ4 + ((-disQ1), 0), PosQ41 + ((-disQ1), 0)) → segQ114
  114. Segment(PosQ1 + ((-disQ1), 0), PosQ41 + ((-disQ1), 0)) → segQ115
  115. Segment(PosQ1 + (If[step ≟ 12, 0, -1.65] - disQ1, 0), PosQ4 + (If[step ≟ 12, 0, -1.65] - disQ1, 0)) → segQ116
  116. Text("\textsf{(a \(-\) b)}", Midpoint[segQ111] + (0, 0.35), false, true, 0, 0) → CapQ111
  117. Text("\textsf{b}", Midpoint[segQ112] + (0, 0.35), false, true, 0, 0) → CapQ112
  118. Text("\textsf{a}", Midpoint[segQ113] + (0, 0.35), false, true, 0, 0) → CapQ113
  119. Text("\textsf{(a \(-\) b)}", Midpoint[segQ114] + (0.1, 0), false, true, -1, 0) → CapQ114
  120. Text("\textsf{b}", Midpoint[segQ115] + (0, 0), false, true, -1, 0) → CapQ115
  121. Text("\textsf{a}", Midpoint[segQ116] + (0, 0), false, true, -1, 0) → CapQ116
  122. Sequence(PosQ41 + (k / 20 * (PosQ23 - PosQ41)) + (dimQ / 2, ((-(1 - parQ)) * dimQ / 2)), k, 0, 25) → PointsP13
  123. Point(PointsP13) → PosP13
  124. Reverse(Sequence[PosQM + (k / 20 * (PosQ2 - PosQ12)) + (((1 - parQ) * dimQ / 2), ((-(1 - parQ)) * dimQ / 2)), k, 0, 60]) → PointsP14
  125. Point(PointsP14) → PosP14
  126. Sequence(Midpoint[PosQ12, PosQ3] + (k / 20 * (PosQ2 - PosQ12)), k, 0, 60) → PointsP15
  127. Point(PointsP15) → PosP15
  128. If(step ≟ 2, correct021 ∧ correct022 ∧ correct023 ∧ correct024, step ≟ 17, PosR1 ≟ Point[segR1, 1], step ≟ 18, PosR2 ≟ Point[segR2, 1], step ≟ 19, correct191 ∧ correct192, step ≟ 3, correct031 ∧ validate ∨ showsolution, step ≟ 8, correct081 ∧ validate08 ∨ showsolution08, step ≟ 6, step ≟ 20, sliderR3 ≟ 1, step ≟ 11, PosP11 ≟ PosQ1, step ≟ 14, correct141 ∧ IndexOf[PosP14, PointsP14] ≟ Length[PointsP14], step ≟ 15, IndexOf[PosP15, PointsP15] ≟ Length[PointsP15], step ≟ 4, PosP041 ≟ PosDD041 ∧ PosP042 ≟ PosDD042, correct06, true, step ≟ 9, correct091, step ≟ 13, IndexOf[PosP13, PointsP13] ≟ Length[PointsP13], step ≟ 16, correct16) → clickableBtnNext
  129. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\→\end{array}}}", PosP13 + (dimQ / 2 - 0.25, 0), false, true, 1, 0) → CapZiehMich13
  130. Text("\textsf{a \cdot b}", PosP13 + (0, 0.05), false, true, 0, 0) → Cap131
  131. Segment(PosQ41, PosQ23) → segQ131
  132. Textfield(input141) → InputBox141
  133. Text("\textsf{a \cdot b}", Midpoint[PosQ34, PosQ2], false, true, 0, 0) → CapQ141
  134. Text("\textsf{b²}", PosP14 + (0, 0.1), false, true, 0, 0) → CapQ142
  135. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\←\end{array}}}", PosP14 + (0, ((1 - parQ) * dimQ / 2) + 0.5), false, true, 0, 0) → CapZiehMich14
  136. PolyLine(PosSB, Corner[txt142, 2] + (0, 0.25), Corner[txt142, 2] + (0, 0), Corner[txt142, 1] + (-0.1, 0), Corner[txt142, 4] + (-0.1, 0.1), Corner[txt142, 3] + (0, 0.1), Corner[txt142, 2] + (0, 0.75), PosSB) → sb142
  137. Text("\textsf{a \cdot b}", PosP15, false, true, 0, 0) → CapQ151
  138. Text("\textsf{\textcolor{#50c1ce}{\bold{Zieh mich!}}", Midpoint[ParkP041, ParkP042] + (0, heightDD04 + 0.5), false, true, 0, 0) → CapZiehMich04
  139. Text("\textsf{1. Binomische Formel\vphantom{g}}", PosP041 + (0, 0.05), false, true, 0, 0) → txtDD041
  140. Text("\textsf{2. Binomische Formel\vphantom{g}}", PosP042 + (0, 0.05), false, true, 0, 0) → txtDD042
  141. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\→\end{array}}}", PosP15 + (0.65, 0), false, true, 1, 0) → CapZiehMich15
  142. IndexOf(PosP14, PointsP14) → indexP14
  143. Text("\textsf{\bold{\begin{array}↑\\Zieh mich!\end{array}}}", (10.95, 3.7), false, true, 0, -1) → CapZiehMichTL

AI Drawing Prompt Reference

Draw a geometric diagram demonstrating the binomial perfect square formula (a-b)²=a²-2ab+b². On the left side of the canvas, there is a large square with side length labeled as 'a', and inside it a smaller square with side length 'b', forming two rectangular regions between them. Two additional rectangles extending to the right and below the large square are labeled as 'a·b'. Below the entire figure, display the formula (a-b)² in large font. Adjust the positions and sizes of the squares and rectangles to visually illustrate the geometric meaning of the perfect square formula.
The prompt above was compiled from the original drawing commands and is for reference only.