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Simplifying Powers with Geometric Construction and Algebraic Manipulation

Simplifying Powers with Geometric Construction and Algebraic Manipulation
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2024-09-16 21:34
In collections Multiplikation von Binomen
This example demonstrates how to simplify power expressions through geometric visualization and algebraic manipulation. Key mathematical concepts include expanding powers, combining like terms, and algebraic simplification. Construction involves using GeoGebra commands like Join, Element, Textfield, Coefficients, and Sequence to build diagrams and handle numerical inputs. Suitable for middle schoo

GeoGebra Commands & Parameters

  1. Join({{2, 1}, 3…numberOfQuestions}) → randomQuestions
  2. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  3. Textfield(InputFunc) → inputBox
  4. Coefficients(Expand[SolFunc]) → CoeffList
  5. Sequence(If[abs(CoeffList(k)) ≠ 1 ∧ CoeffList(k) ≠ 0, Defined[IndexOf[("" * abs(CoeffList(k))), Text[inputBox]]], true], k, 1, Length[CoeffList]) → InputCoeffList
  6. RemoveUndefined({SolFunc1, SolFunc2, SolFunc3, SolFunc4}) → SolFuncList
  7. RemoveUndefined({Func1, Func2, Func3, Func4, Func5, Func6, Func7, Func8}) → FuncList
  8. Textfield(InputFunc2) → inputBox2
  9. If(showIB1 ∧ showIB2, correct1 ∧ correct2, correct2) → correct
  10. If((If[PosX1(randomQuestion) ≟ 1, 1, SignList1(randomQuestion)] * If[PosX2(randomQuestion) ≟ 1, 1, SignList2(randomQuestion)]) ∈ {1, 4}, "", "\(-\)") → TxtSolSign1
  11. Sequence(If[CoeffList(k) ≠ 0, Defined[IndexOf[((("" * VarList(randomQuestion)) * "^") * k), Text[inputBox]]], true], k, 1, Length[CoeffList] - 1) → PotVarList
  12. CircleArc(Midpoint[Pos1, Pos2] + (0, -0.65), Pos2, Pos1) → arc11
  13. CircleArc(Midpoint[Pos1, Pos3] + (0, -0.65), Pos3, Pos1) → arc21
  14. CircleArc(Midpoint[Pos4, Pos5] + (0, 0.4), Pos4, Pos5) → arc12
  15. CircleArc(Midpoint[Pos4, Pos6] + (0, 0.4), Pos4, Pos6) → arc22
  16. Expand(SolFunc) → SolEx
  17. Split(Text[SolEx], {"-", "+"}) → SolFuncTxt
  18. Split(Text[inputBox2], {"-", "+"}) → FuncTxt
  19. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (800, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  20. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  21. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-0.43000000000000016, 10.739999999999997), (0.9066750208855479, 10.739999999999997), (2.243350041771096, 10.739999999999997), (3.580025062656643, 10.739999999999997), (4.916700083542192, 10.739999999999997), (6.2533751044277395, 10.739999999999997), (7.590050125313287, 10.739999999999997), (8.926725146198836, 10.739999999999997), (10.263400167084384, 10.739999999999997), (11.600075187969932, 10.739999999999997), (12.93675020885548, 10.739999999999997), (14.273425229741028, 10.739999999999997), (15.610100250626573, 10.739999999999997)}, {(-0.43000000000000016, 9.40220735785953), (0.9066750208855479, 9.40220735785953), (2.243350041771096, 9.40220735785953), (3.580025062656643, 9.40220735785953), (4.916700083542192, 9.40220735785953), (6.2533751044277395, 9.40220735785953), (7.590050125313287, 9.40220735785953), (8.926725146198836, 9.40220735785953), (10.263400167084384, 9.40220735785953), (11.600075187969932, 9.40220735785953), (12.93675020885548, 9.40220735785953), (14.273425229741028, 9.40220735785953), (15.610100250626573, 9.40220735785953)}, {(-0.43000000000000016, 8.064414715719062), (0.9066750208855479, 8.064414715719062), (2.243350041771096, 8.064414715719062), (3.580025062656643, 8.064414715719062), (4.916700083542192, 8.064414715719062), (6.2533751044277395, 8.064414715719062), (7.590050125313287, 8.064414715719062), (8.926725146198836, 8.064414715719062), (10.263400167084384, 8.064414715719062), (11.600075187969932, 8.064414715719062), (12.93675020885548, 8.064414715719062), (14.273425229741028, 8.064414715719062), (15.610100250626573, 8.064414715719062)}, {(-0.43000000000000016, 6.726622073578595), (0.9066750208855479, 6.726622073578595), (2.243350041771096, 6.726622073578595), (3.580025062656643, 6.726622073578595), (4.916700083542192, 6.726622073578595), (6.2533751044277395, 6.726622073578595), (7.590050125313287, 6.726622073578595), (8.926725146198836, 6.726622073578595), (10.263400167084384, 6.726622073578595), (11.600075187969932, 6.726622073578595), (12.93675020885548, 6.726622073578595), (14.273425229741028, 6.726622073578595), (15.610100250626573, 6.726622073578595)}, {(-0.43000000000000016, 5.388829431438127), (0.9066750208855479, 5.388829431438127), (2.243350041771096, 5.388829431438127), (3.580025062656643, 5.388829431438127), (4.916700083542192, 5.388829431438127), (6.2533751044277395, 5.388829431438127), (7.590050125313287, 5.388829431438127), (8.926725146198836, 5.388829431438127), (10.263400167084384, 5.388829431438127), (11.600075187969932, 5.388829431438127), (12.93675020885548, 5.388829431438127), (14.273425229741028, 5.388829431438127), (15.610100250626573, 5.388829431438127)}, {(-0.43000000000000016, 4.051036789297659), (0.9066750208855479, 4.051036789297659), (2.243350041771096, 4.051036789297659), (3.580025062656643, 4.051036789297659), (4.916700083542192, 4.051036789297659), (6.2533751044277395, 4.051036789297659), (7.590050125313287, 4.051036789297659), (8.926725146198836, 4.051036789297659), (10.263400167084384, 4.051036789297659), (11.600075187969932, 4.051036789297659), (12.93675020885548, 4.051036789297659), (14.273425229741028, 4.051036789297659), (15.610100250626573, 4.051036789297659)}, {(-0.43000000000000016, 2.7132441471571926), (0.9066750208855479, 2.7132441471571926), (2.243350041771096, 2.7132441471571926), (3.580025062656643, 2.7132441471571926), (4.916700083542192, 2.7132441471571926), (6.2533751044277395, 2.7132441471571926), (7.590050125313287, 2.7132441471571926), (8.926725146198836, 2.7132441471571926), (10.263400167084384, 2.7132441471571926), (11.600075187969932, 2.7132441471571926), (12.93675020885548, 2.7132441471571926), (14.273425229741028, 2.7132441471571926), (15.610100250626573, 2.7132441471571926)}, {(-0.43000000000000016, 1.3754515050167253), (0.9066750208855479, 1.3754515050167253), (2.243350041771096, 1.3754515050167253), (3.580025062656643, 1.3754515050167253), (4.916700083542192, 1.3754515050167253), (6.2533751044277395, 1.3754515050167253), (7.590050125313287, 1.3754515050167253), (8.926725146198836, 1.3754515050167253), (10.263400167084384, 1.3754515050167253), (11.600075187969932, 1.3754515050167253), (12.93675020885548, 1.3754515050167253), (14.273425229741028, 1.3754515050167253), (15.610100250626573, 1.3754515050167253)}, {(-0.43000000000000016, 0.03765886287625797), (0.9066750208855479, 0.03765886287625797), (2.243350041771096, 0.03765886287625797), (3.580025062656643, 0.03765886287625797), (4.916700083542192, 0.03765886287625797), (6.2533751044277395, 0.03765886287625797), (7.590050125313287, 0.03765886287625797), (8.926725146198836, 0.03765886287625797), (10.263400167084384, 0.03765886287625797), (11.600075187969932, 0.03765886287625797), (12.93675020885548, 0.03765886287625797), (14.273425229741028, 0.03765886287625797), (15.610100250626573, 0.03765886287625797)}, {(-0.43000000000000016, -1.3001337792642094), (0.9066750208855479, -1.3001337792642094), (2.243350041771096, -1.3001337792642094), (3.580025062656643, -1.3001337792642094), (4.916700083542192, -1.3001337792642094), (6.2533751044277395, -1.3001337792642094), (7.590050125313287, -1.3001337792642094), (8.926725146198836, -1.3001337792642094), (10.263400167084384, -1.3001337792642094), (11.600075187969932, -1.3001337792642094), (12.93675020885548, -1.3001337792642094), (14.273425229741028, -1.3001337792642094), (15.610100250626573, -1.3001337792642094)}}
  22. Text("$\textsf{ausmultiplizieren}$", PosTxtIB + (6, -0.2), false, true, 1, 0) → txtCap1
  23. Text("$\textsf{zusammenfassen\phantom{p}}$", PosTxtIB + (0, -1.5) + (6, -0.2), false, true, 1, 0) → txtCap2
  24. If(showIB1, PosTxtIB + (0, -1.5), PosTxtIB) → PosIB2