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Cubic Binomial Expansion

Cubic Binomial Expansion
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2025-01-09 19:34
CalculusDerivative
In collections Binomische Formeln
This example demonstrates how to use the cubic binomial expansion to calculate the power of a binomial. The user can input any binomial expression, and the system will automatically expand and calculate the result. The core mathematical concepts involved are the cubic binomial expansion and the calculation of binomial powers. The construction points include using the Expand command in GeoGebra to expand the binomial expression, and using the Text command to display the result. This example is suitable for middle school and high school mathematics, particularly algebra and number theory.

GeoGebra Commands & Parameters

  1. Expand(TaskFunc) → solFunc
  2. Text(inputFunc) → txtInput
  3. Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{3, 2, 1}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}}
  4. Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}}
  5. Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}}
  6. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList1(Order1(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList1(Order1(3))) * "\vphantom{gb²}}$")}}) → dropdown1
  7. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList3(Order3(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList3(Order3(3))) * "\vphantom{gb²}}$")}}) → dropdown3
  8. Join({{"$\textsf{\phantom{144\:b² }\vphantom{gb²}}$"}, {(("$\textsf{" * DDList2(Order2(1))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(2))) * " }\vphantom{gb²}$"), (("$\textsf{" * DDList2(Order2(3))) * "\vphantom{gb²}}$")}}) → dropdown2
  9. SelectedIndex(dropdown1) → indexdd1
  10. SelectedIndex(dropdown2) → indexdd2
  11. SelectedIndex(dropdown3) → indexdd3
  12. SelectedIndex(dropdownSign1) → indexddS1
  13. SelectedIndex(dropdownSign2) → indexddS2
  14. If(Case ≠ 3, indexdd2 - 1 ≟ IndexOf[1, Order2], true) → correctdd2
  15. If(Case ≠ 3, indexddS2 ≟ 2, true) → correctddS2
  16. If(step ≟ 1, correctExtend ∧ correctValue, correctdd1 ∧ correctdd2 ∧ correctdd3 ∧ correctddS1 ∧ correctddS2) → correct
  17. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {6, 5, 3, 9, 2, 10, 4, 1, 8, 2}
  18. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  19. If(step ≟ 1, Defined[inputFunc], indexdd1 ≠ 1 ∧ If[Case ≟ 3, true, indexdd2 ≠ 1] ∧ indexdd3 ≠ 1 ∧ indexddS1 ≠ 1 ∧ If[Case ≟ 3, true, indexddS2 ≠ 1]) → clickableBtnValidate
  20. Textfield(inputFunc) → inputBox
  21. If(questionCount ∈ {1, 3, 5, 6, 8, 11}, SignList(1), SignList(2)) → sign1
  22. If(questionCount ∈ {1, 3, 5, 6, 8, 11}, SignList(2), SignList(1)) → sign2
  23. If(CaseVar ≟ 2, "", var1) → txtVar1
  24. If(CaseVar ≟ 1, "", var2) → txtVar2
  25. Invert(pixMat) → invPixMat
  26. If(Case ≟ 3, PosDDS1 + (1.42, 0), PosDDS2 + (1.42, 0)) → PosDD3
  27. ReplaceAll(Text[Expand[TaskFunc]], "-", "+") → txtHint3

AI Drawing Prompt Reference

Need to draw an interactive mathematical calculation interface to demonstrate cubic binomial expansion. The interface includes an input box where users can enter any binomial expression, a text display area that automatically shows the expanded result, three dropdown menus listing different permutation order options, a validation button to check if input is correct, and some text labels for instructions. The construction order is: first create the input box and text display area, then generate permutation lists and fill the dropdown menus, then add the validation button, and finally adjust layout and labels.
The prompt above was compiled from the original drawing commands and is for reference only.