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二项式公式几何推导：正方形面积法

二项式公式几何推导：正方形面积法
几何画板及绘图内容加载中，请稍等……
2025-09-23 23:35
多边形函数不等式几何作图函数图像
所属专题 Binomische Formeln
本范例通过矩形与正方形的面积关系，图形化推导第二个二项式公式(a-b)²=a²-2ab+b²。核心数学概念包括完全平方公式、面积法证明、整式运算。作图要点：使用Polygon绘制代表a²的大正方形和代表b²的小正方形，通过Rectangle/Polygon构造两个ab面积的矩形，利用Textfield显示公式推导步骤，设置InputBox供学生输入(5-h)²和(2c-3d)²的计算结果，同时提供排序练习帮助学生理解几何推导逻辑。适合7-8年级学生，用于理解完全平方公式的几何意义，培养数形结合思想。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {6, 2, 4, 4, 7, 6, 4, 1, 7, 3}
  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. Midpoint(PosA, PosC) → MPQuadrat
  19. Segment(MPQuadrat + (0.45, 0.45), PosC) → Diagonale1
  20. Point(Diagonale1) → PosP
  21. Segment(PosA + (0, If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, (-disCap1), (-disCap2)]), PosB + (0, If[step ≟ 11 ∨ step ≟ 12 ∧ PosP ≟ PosC, (-disCap1), (-disCap2)])) → segCap111
  22. 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
  23. Text("\textsf{a}", Midpoint[segCap112], false, true, 1, 0) → Cap112
  24. Segment(PosA + (0, (-disCap1)), PosP1 + (0, (-disCap1))) → segCap121
  25. Segment(PosB + (0, (-disCap1)), PosP1 + (0, (-disCap1))) → segCap122
  26. Segment(PosB + (disCap1, 0), PosP2 + (disCap1, 0)) → segCap123
  27. Segment(PosC + (disCap1, 0), PosP2 + (disCap1, 0)) → segCap124
  28. Text("\textsf{a \(-\) b}", Midpoint[segCap123], false, true, 1, 0) → Cap123
  29. Text("\textsf{b}", Midpoint[segCap124], false, true, 1, 0) → Cap124
  30. Text("\textsf{a}", Midpoint[segCap111] + (0, 0.05), false, true, 0, -1) → Cap111
  31. Text("\textsf{a \(-\) b}", Midpoint[segCap121] + (0, 0.05), false, true, 0, -1) → Cap121
  32. Text("\textsf{b}", Midpoint[segCap122] + (0, 0.05), false, true, 0, -1) → Cap122
  33. Segment(PosP1, PosP1 + (sidelength + 4, 0)) → segR1
  34. Point(segR1) → PosR1
  35. Polygon(PosR1, PosR1 + (2.049999999999999, 0), PosR1 + (2.049999999999999, 0) + (0, sidelength), PosR1 + (0, sidelength)) → polyR1, f, g, h, b
  36. Segment(PosP4, PosP4 + (sidelength + 4, 0)) → segR2
  37. Point(segR2) → PosR2
  38. Polygon(PosR2, PosR2 + (sidelength, 0), PosR2 + PosC - PosP2 + (sidelength, 0), PosR2 + PosC - PosP2) → polyR2, posr2, i, j, k
  39. 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
  40. Text("\textsf{(a \(-\) b)²}", PosDD1 + (0, 0.1), false, true, 0, 0) → txtDD1
  41. 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
  42. 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
  43. Text("\textsf{\colorbox{white}{a \cdot b}}", PosR1 + (0.5 * (PosB - PosP1)) + (0.5 * (PosP2 - PosB)), false, true, 0, 0) → CapR1
  44. Text("\textsf{\colorbox{white}{a \cdot b}}", PosR2 + (0.5 * (PosP1 - PosA)) + (0.5 * (PosC - PosP2)), false, true, 0, 0) → CapR2
  45. PolyLine(PosR2, PosR2 + PosP1 - PosA, PosR1) → PL20
  46. PolyLine(PosR3 + {(0, 0), PosP2 - PosP, PosC - PosP, PosP3 - PosP, (0, 0)}) → PLB4R
  47. 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
  48. Textfield(input021) → InputBox021
  49. Textfield(input022) → InputBox022
  50. 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}}$"}, OrderDD061) → dropdown061
  51. SelectedIndex(dropdown061) → index061
  52. Sort({"$\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}}$"}, OrderDD062) → dropdown062
  53. SelectedIndex(dropdown062) → index062
  54. Sort({"$\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}}$"}, OrderDD063) → dropdown063
  55. SelectedIndex(dropdown063) → index063
  56. Sort({"$\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}}$"}, OrderDD064) → dropdown064
  57. SelectedIndex(dropdown064) → index064
  58. PathParameter(PosP) → parP
  59. Join({{1}, Shuffle[2…5]}) → OrderDD161
  60. Sort({"$\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)}}$"}, OrderDD161) → dropdown161
  61. SelectedIndex(dropdown161) → index161
  62. Join({{1}, Shuffle[2…5]}) → OrderDD162
  63. Sort({"$\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)}}$"}, OrderDD162) → dropdown162
  64. SelectedIndex(dropdown162) → index162
  65. Join({{1}, Shuffle[2…5]}) → OrderDD191
  66. Sort({"$\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)}}$"}, OrderDD191) → dropdown191
  67. SelectedIndex(dropdown191) → index191
  68. Join({{1}, Shuffle[2…5]}) → OrderDD192
  69. Sort({"$\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
  70. SelectedIndex(dropdown192) → index192
  71. PointIn(polyLight2) → Light08
  72. Circle(Light08, radius) → CTaschenlampe081
  73. If(correct061 ∧ correct062 ∧ correct063, 4, correct061 ∧ correct062, 3, correct061, 2, 1) → step6
  74. CircleArc(Midpoint[PosCalc11, PosCalc14] + (0, dis6), PosCalc14, PosCalc11) → arc062
  75. CircleArc(Midpoint[PosCalc11, PosCalc13] + (0, dis6), PosCalc13, PosCalc11) → arc061
  76. 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
  77. Circle(PointListMinus(2), radius) → sol031
  78. 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
  79. 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
  80. Mirror(CircleArc[Midpoint[PosCalc12, PosCalc13] + (0, dis6), PosCalc13, PosCalc12], SpiegelGerade) → arc063
  81. Mirror(CircleArc[Midpoint[PosCalc12, PosCalc14] + (0, dis6), PosCalc14, PosCalc12], SpiegelGerade) → arc064
  82. Text("\textsf{(a \(-\) b)²}", Midpoint[PosA, PosP] + (0, 0.1), false, true, 0, 0) → txt152
  83. Text("\textsf{\bold{Zieh mich!}}", PosP + (0.4, 0.3), false, true, 1, 0) → CapP12
  84. Segment(PosP + (-0.25, -0.25), PosP + (-0.75, -0.75)) → arrow12
  85. Textfield(input024) → InputBox024
  86. Textfield(input091) → InputBox091
  87. Text("\textsf{\bold{Zieh mich!}}", (11.5, 3.5) + (0, 1.25), false, true, 0, 0) → CapDD14
  88. Segment(Midpoint[Corner[CapDD14, 1], Corner[CapDD14, 2]], Midpoint[Corner[CapDD14, 1], Corner[CapDD14, 2]] + (0, -0.34)) → arrowDD14
  89. 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
  90. 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
  91. Circle(Light08, radius) → CTaschenlampe082
  92. Line(MPTaschenlampe, Light08) → GTaschenlampe08
  93. Intersect(CTaschenlampe3, GTaschenlampe08, 2) → PosTL081
  94. Intersect(CTaschenlampe3, GTaschenlampe08, 1) → PosTL082
  95. Rotate(PosTL082 + (0.2 * UnitOrthogonalVector[GTaschenlampe08]), -67°, MPTaschenlampe) → PosImgTaschenlampe082
  96. Tangent(PosTL082, CTaschenlampe081) → tangent081, tangent082
  97. Circle(PointList08(2) + (0.1, 0), radius) → sol081
  98. 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
  99. 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
  100. 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
  101. 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
  102. 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
  103. 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
  104. 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
  105. 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
  106. Sequence(PosQ4 + (k / 20 * (PosQ1 - PosQ4)), k, 0, 20) → PointsP11
  107. Point(PointsP11) → PosP11
  108. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\↓\end{array}}}", PosP11 + (-0.25, 0), false, true, 1, -1) → CapZiehMich11
  109. Segment(PosQ4 + (0, disQ1), PosQ34 + (0, disQ1)) → segQ111
  110. Segment(PosQ3 + (0, disQ1), PosQ34 + (0, disQ1)) → segQ112
  111. Segment(PosQ3 + (0, If[step ≟ 12, 0, 0.65] + disQ1), PosQ4 + (0, If[step ≟ 12, 0, 0.65] + disQ1)) → segQ113
  112. Segment(PosQ4 + ((-disQ1), 0), PosQ41 + ((-disQ1), 0)) → segQ114
  113. Segment(PosQ1 + ((-disQ1), 0), PosQ41 + ((-disQ1), 0)) → segQ115
  114. Segment(PosQ1 + (If[step ≟ 12, 0, -1.65] - disQ1, 0), PosQ4 + (If[step ≟ 12, 0, -1.65] - disQ1, 0)) → segQ116
  115. Text("\textsf{(a \(-\) b)}", Midpoint[segQ111] + (0, 0.35), false, true, 0, 0) → CapQ111
  116. Text("\textsf{b}", Midpoint[segQ112] + (0, 0.35), false, true, 0, 0) → CapQ112
  117. Text("\textsf{a}", Midpoint[segQ113] + (0, 0.35), false, true, 0, 0) → CapQ113
  118. Text("\textsf{(a \(-\) b)}", Midpoint[segQ114] + (0.1, 0), false, true, -1, 0) → CapQ114
  119. Text("\textsf{b}", Midpoint[segQ115] + (0, 0), false, true, -1, 0) → CapQ115
  120. Text("\textsf{a}", Midpoint[segQ116] + (0, 0), false, true, -1, 0) → CapQ116
  121. Sequence(PosQ41 + (k / 20 * (PosQ23 - PosQ41)) + (dimQ / 2, ((-(1 - parQ)) * dimQ / 2)), k, 0, 25) → PointsP13
  122. Point(PointsP13) → PosP13
  123. Reverse(Sequence[PosQM + (k / 20 * (PosQ2 - PosQ12)) + (((1 - parQ) * dimQ / 2), ((-(1 - parQ)) * dimQ / 2)), k, 0, 60]) → PointsP14
  124. Point(PointsP14) → PosP14
  125. Sequence(Midpoint[PosQ12, PosQ3] + (k / 20 * (PosQ2 - PosQ12)), k, 0, 60) → PointsP15
  126. Point(PointsP15) → PosP15
  127. 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
  128. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\→\end{array}}}", PosP13 + (dimQ / 2 - 0.25, 0), false, true, 1, 0) → CapZiehMich13
  129. Text("\textsf{a \cdot b}", PosP13 + (0, 0.05), false, true, 0, 0) → Cap131
  130. Segment(PosQ41, PosQ23) → segQ131
  131. Textfield(input141) → InputBox141
  132. Text("\textsf{a \cdot b}", Midpoint[PosQ34, PosQ2], false, true, 0, 0) → CapQ141
  133. Text("\textsf{b²}", PosP14 + (0, 0.1), false, true, 0, 0) → CapQ142
  134. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\←\end{array}}}", PosP14 + (0, ((1 - parQ) * dimQ / 2) + 0.5), false, true, 0, 0) → CapZiehMich14
  135. 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
  136. Text("\textsf{a \cdot b}", PosP15, false, true, 0, 0) → CapQ151
  137. Text("\textsf{\textcolor{#50c1ce}{\bold{Zieh mich!}}", Midpoint[ParkP041, ParkP042] + (0, heightDD04 + 0.5), false, true, 0, 0) → CapZiehMich04
  138. Text("\textsf{1. Binomische Formel\vphantom{g}}", PosP041 + (0, 0.05), false, true, 0, 0) → txtDD041
  139. Text("\textsf{2. Binomische Formel\vphantom{g}}", PosP042 + (0, 0.05), false, true, 0, 0) → txtDD042
  140. Text("\textsf{\bold{\begin{array}{c}Zieh mich!\\→\end{array}}}", PosP15 + (0.65, 0), false, true, 1, 0) → CapZiehMich15
  141. IndexOf(PosP14, PointsP14) → indexP14
  142. PolyLine(PosSB, Corner[txt102, 2] + (0, 0.5), 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, 0.75), PosSB) → sb10

AI 绘图提示语参考

请绘制一个展示(a-b)^2 = a^2 - 2ab + b^2几何推导的图形。图形应包含两个正方形，分别代表a^2和b^2，以及两个矩形，每个矩形面积为ab。两个矩形应与正方形通过线段连接，形成完整的面积模型。正方形和矩形应标注相应的文本，如"a^2"、"b^2"、"a*b"等。图形应清晰展示展开与组合的过程，帮助理解公式。构造顺序为：先绘制两个正方形，再绘制两个矩形，然后连接各部分，最后添加文本标签。
以上提示语为根据原始绘图命令整理而来，仅供参考。