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Calculating with Binomial Formulas

Calculating with Binomial Formulas
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2024-07-01 17:15
Function
In collections Binomische Formeln
This example demonstrates how to use binomial formulas to calculate powers of algebraic expressions. Key math concepts include the binomial theorem, algebraic operations, and expression simplification. GeoGebra commands/objects used in construction include Expand, Text, Flatten, Random, Sequence, Join, SelectedIndex, If, Element, Textfield, and Invert. It is suitable for 7-8 grade students to practice and reinforce the application of the binomial theorem through interactive operations, deepening their understanding.

GeoGebra Commands & Parameters

  1. Expand(TaskFunc) → solFunc
  2. Text(inputFunc) → txtInput
  3. Flatten(Join[{{1, 1, 2, 2, 3, 3}, Sequence[Shuffle[1…3], k, 1, 34]}]) → CaseList
  4. Random(1, 12, 100) → ParList1, {1, 5, 7, 8, 11, 7, 7, 2, 7, 9, 4, 4, 9, 7, 12, 8, 1, 4, 9, 8, 2, 7, 9, 10, 12, 7, 11, 10, 1, 9, 6, 8, 6, 5, 9, 3, 11, 6, 12, 10, 9, 7, 7, 11, 8, 6, 8, 2, 1, 10, 3, 8, 4, 6, 3, 7, 3, 1, 8, 7, 4, 5, 5, 11, 6, 2, 4, 6, 4, 4, 4, 10, 2, 5, 11, 3, 1, 5, 4, 4, 5, 4, 12, 7, 9, 3, 2, 11, 11, 12, 5, 6, 11, 11, 11, 6, 12, 6, 7, 9}
  5. Sequence(RandomElement[Remove[1…12, {ParList1(k)}]], k, 1, 100) → ParList2, {9, 2, 5, 5, 2, 3, 10, 6, 3, 12, 8, 12, 7, 11, 7, 5, 4, 2, 2, 7, 7, 10, 7, 8, 7, 6, 1, 7, 7, 5, 7, 12, 9, 7, 12, 5, 3, 8, 11, 7, 5, 8, 5, 10, 5, 7, 10, 1, 4, 11, 8, 1, 10, 2, 6, 3, 10, 10, 7, 10, 9, 7, 4, 12, 11, 9, 10, 3, 3, 8, 9, 3, 12, 12, 9, 4, 5, 10, 8, 6, 8, 7, 8, 1, 7, 10, 4, 10, 3, 1, 8, 7, 8, 8, 5, 1, 6, 8, 9, 7}
  6. Sequence(RandomElement[Alphabet], k, 1, 100) → VarList1, {"s", "e", "w", "z", "s", "z", "q", "e", "f", "d", "x", "t", "z", "g", "j", "c", "x", "r", "j", "f", "e", "c", "q", "y", "t", "d", "d", "h", "u", "i", "j", "y", "u", "r", "f", "d", "v", "j", "r", "f", "d", "d", "j", "v", "f", "s", "z", "d", "v", "t", "s", "s", "y", "e", "g", "h", "f", "j", "z", "y", "g", "h", "r", "y", "w", "c", "h", "z", "r", "s", "h", "g", "g", "h", "v", "q", "d", "i", "g", "r", "f", "f", "z", "y", "z", "z", "u", "d", "x", "j", "v", "u", "z", "h", "w", "e", "s", "f", "s", "w"}
  7. Random(1, 3, 100) → CaseVarList, {1, 1, 3, 3, 3, 2, 2, 2, 2, 3, 1, 2, 3, 2, 1, 3, 3, 2, 3, 1, 1, 2, 2, 3, 3, 3, 3, 1, 2, 1, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 2, 2, 3, 1, 1, 2, 3, 2, 1, 3, 1, 3, 2, 3, 1, 1, 3, 2, 2, 2, 1, 3, 1, 3, 2, 1, 1, 1, 3, 1, 2, 3, 1, 1, 1, 3, 3, 2, 1, 2, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3}
  8. Sequence(RandomElement[Remove[Alphabet, {VarList1(k)}]], k, 1, 100) → VarList2, {"y", "v", "x", "h", "t", "e", "c", "w", "c", "x", "z", "i", "c", "j", "y", "v", "q", "s", "d", "h", "d", "f", "g", "s", "d", "v", "i", "u", "z", "t", "c", "c", "i", "i", "s", "r", "u", "h", "c", "r", "s", "i", "t", "y", "s", "x", "j", "q", "e", "f", "g", "w", "g", "r", "q", "c", "u", "z", "j", "u", "e", "c", "d", "r", "c", "g", "q", "i", "f", "h", "x", "u", "y", "u", "c", "w", "t", "z", "v", "h", "h", "v", "v", "h", "j", "u", "r", "r", "f", "t", "e", "e", "w", "g", "q", "r", "g", "q", "y", "j"}
  9. Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}}
  10. Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}}
  11. Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {3, 2, 1}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {3, 2, 1}}
  12. 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
  13. 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
  14. 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
  15. SelectedIndex(dropdown1) → indexdd1
  16. SelectedIndex(dropdown2) → indexdd2
  17. SelectedIndex(dropdown3) → indexdd3
  18. SelectedIndex(dropdownSign1) → indexddS1
  19. SelectedIndex(dropdownSign2) → indexddS2
  20. If(Case ≠ 3, indexdd2 - 1 ≟ IndexOf[1, Order2], true) → correctdd2
  21. If(Case ≠ 3, indexddS2 ≟ 2, true) → correctddS2
  22. If(step ≟ 1, correctExtend ∧ correctValue, correctdd1 ∧ correctdd2 ∧ correctdd3 ∧ correctddS1 ∧ correctddS2) → correct
  23. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {6, 10, 7, 8, 6, 8, 8, 6, 1, 10}
  24. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  25. If(step ≟ 1, Defined[inputFunc], indexdd1 ≠ 1 ∧ If[Case ≟ 3, true, indexdd2 ≠ 1] ∧ indexdd3 ≠ 1 ∧ indexddS1 ≠ 1 ∧ If[Case ≟ 3, true, indexddS2 ≠ 1]) → clickableBtnValidate
  26. Join(Sequence[Shuffle[1…5], k, 1, 20]) → KidsList
  27. Textfield(inputFunc) → inputBox
  28. If(CaseVar ≟ 2, "", var1) → txtVar1
  29. If(CaseVar ≟ 1, "", var2) → txtVar2
  30. Invert(pixMat) → invPixMat
  31. If(Case ≟ 3, PosDDS1 + (1.42, 0), PosDDS2 + (1.42, 0)) → PosDD3

AI Drawing Prompt Reference

Create 100 random polynomials with random letters and numbers, display their expansions, and allow users to select and validate them. First, generate 100 random letters and numbers, then randomly create polynomials and display them in dropdown menus. Users can select a polynomial and the system will validate their choice.
The prompt above was compiled from the original drawing commands and is for reference only.