MathPlotAI Logo MathPlotAI

Expanding with the 2nd Binomial Formula: Interactive (a+b)^2 Calculation

Expanding with the 2nd Binomial Formula: Interactive (a+b)^2 Calculation
Loading the math board and drawing, please wait…
2025-01-09 19:34
FunctionSequenceTransformationGeometric ConstructionGraphing
In collections Binomische Formeln
This GeoGebra example demonstrates how to expand the second binomial square formula, turning expressions like (a+b)^2 into an equivalent polynomial and checking the result. It focuses on key algebra skills: applying binomial identities, reasoning about powers, and performing symbolic expansion and equivalent transformations, reinforced by immediate correctness feedback. Construction and interaction use an input text field where students enter candidate expressions or powers; the app then applies Expand to compute the formal expansion. Text objects (via Text) show prompts and results, while Sequence and Join help structure multi-step content. Conditional logic (SelectedIndex, If, Element, Case/CaseList) selects the appropriate sign/parameter case, and parameter lists (VarList/ParList with var1/var2 and par1/par2) manage variables and coefficients. ReplaceAll and Invert support expression/text transformations for presentation and matching. Student interaction is enabled through Textfield and the task includes counters such as attemptCount, questionCount, and correctCount. Suitable for middle school (grades 7–8) algebra practice, formula teaching, and self-check exercises.

GeoGebra Commands & Parameters

  1. Expand(TaskFunc) → solFunc
  2. Text(inputFunc) → txtInput
  3. Sequence(Shuffle[1…3], k, 1, 100) → OrderList1, {{1, 3, 2}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {3, 2, 1}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {1, 3, 2}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {3, 2, 1}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {3, 2, 1}, {1, 3, 2}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {2, 1, 3}}
  4. Sequence(Shuffle[1…3], k, 1, 100) → OrderList2, {{2, 3, 1}, {2, 3, 1}, {1, 3, 2}, {1, 3, 2}, {3, 1, 2}, {3, 1, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {3, 2, 1}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {3, 2, 1}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 3, 2}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {3, 2, 1}, {1, 3, 2}, {3, 1, 2}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {2, 1, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {2, 3, 1}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}, {2, 3, 1}}
  5. Sequence(Shuffle[1…3], k, 1, 100) → OrderList3, {{1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 1, 2}, {3, 1, 2}, {2, 3, 1}, {2, 3, 1}, {2, 3, 1}, {1, 2, 3}, {1, 2, 3}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {3, 2, 1}, {3, 2, 1}, {3, 1, 2}, {1, 2, 3}, {1, 3, 2}, {1, 3, 2}, {2, 1, 3}, {1, 3, 2}, {1, 2, 3}, {2, 1, 3}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {3, 2, 1}, {2, 1, 3}, {2, 1, 3}, {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}, {3, 1, 2}, {2, 1, 3}, {1, 2, 3}, {2, 3, 1}, {2, 3, 1}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {2, 1, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {2, 3, 1}, {1, 3, 2}, {3, 2, 1}, {1, 3, 2}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {3, 2, 1}, {3, 2, 1}, {2, 3, 1}, {1, 2, 3}, {1, 2, 3}, {3, 1, 2}, {2, 1, 3}, {3, 1, 2}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {2, 3, 1}, {1, 3, 2}, {2, 3, 1}, {2, 3, 1}, {2, 1, 3}, {2, 1, 3}, {2, 3, 1}, {1, 2, 3}, {2, 3, 1}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {1, 2, 3}, {3, 2, 1}, {1, 2, 3}, {1, 2, 3}, {1, 2, 3}}
  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, {10, 4, 7, 4, 5, 2, 2, 1, 6, 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
  25. ReplaceAll(Text[Expand[TaskFunc]], "+", "-") → txtHint3

AI Drawing Prompt Reference

Create an interactive exercise for expanding a binomial square. First, enter the expanded result of (a+b)^2 in the input field. Then, select three randomly ordered options to match the expanded result. Next, choose the correct sign options. Finally, verify if your answer is correct. Note that the system will provide feedback based on your input after each attempt.
The prompt above was compiled from the original drawing commands and is for reference only.