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Practice with the First Binomial Formula

Practice with the First Binomial Formula
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2025-01-09 19:34
FunctionSequenceGraphing
In collections Binomische Formeln
This GeoGebra example is an interactive algebra exercise designed to help students master the first binomial formula, i.e., (a+b)² = a² + 2ab + b². It allows learners to input expanded powers into a text field and receive immediate validation, with step-by-step hints and feedback. The core mathematical concepts include the binomial theorem, polynomial expansion, algebraic expression simplification, and identification of variables and coefficients. In terms of construction, the example uses the Expand command for symbolic expansion, Text and Textfield objects to create the input interface, Sequence and Join to generate problem sets, If and Element for conditional checking and answer matching, and SelectedIndex and Invert to control options and states. Multiple lists (such as ParList1, VarList1) manage randomly generated variables and parameters, while dropdownSign1 and dropdownSign2 provide sign selection, and OrderList/Order are used for sorting and verification. This exercise is suitable for middle school students in grades 7-8, for classroom practice or homework, aiming to deepen understanding and application of the binomial formula through an interactive, visual approach.

GeoGebra Commands & Parameters

  1. Expand(TaskFunc) → solFunc
  2. Text(inputFunc) → txtInput
  3. Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}}
  4. Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}}
  5. Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {2, 3, 1}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {3, 2, 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, {2, 4, 6, 6, 8, 3, 2, 7, 9, 1}
  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(CaseVar ≟ 2, "", var1) → txtVar1
  22. If(CaseVar ≟ 1, "", var2) → txtVar2
  23. Invert(pixMat) → invPixMat
  24. If(Case ≟ 3, PosDDS1 + (1.42, 0), PosDDS2 + (1.42, 0)) → PosDD3

AI Drawing Prompt Reference

This is an interactive algebra practice interface designed to help students master the binomial formula. The interface includes a text input box where students can enter the expanded algebraic expression, a display area showing a randomly generated binomial problem such as (a+b)^2, and a verification feedback area that confirms correct answers. It also features dropdown menus for symbol selection and sorting options to control problem generation and validation logic. The construction order is: first create the input box and problem display area, then generate random problems using lists, add verification conditions, and finally adjust the layout for interactive functionality.
The prompt above was compiled from the original drawing commands and is for reference only.