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Product of Two Trinomials - Visual

Product of Two Trinomials - Visual
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2016-03-24 02:29
TrigonometryCoordinate GeometryOptimizationGeometric Construction
In collections Geom. & Alg.: Quadratics
This example visually demonstrates the product of two trinomials using an area model. It involves core math concepts like polynomial multiplication, area calculation, and geometric representation. Constructed with GeoGebra commands/objects such as Ray, OrthogonalLine, Circle, Intersect, Polygon, and PointIn. Suitable for high school mathematics teaching to understand the geometric meaning of polynomial multiplication and optimization problems.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Circle(A, VA) → c
  4. Intersect(c, b) → C, D
  5. Circle(D, VB) → d
  6. Intersect(d, b) → E, F
  7. Circle(F, VC) → e
  8. Intersect(e, b, 2) → G
  9. Circle(A, HA) → f
  10. Intersect(f, a, 1) → H
  11. Circle(H, HB) → g
  12. Intersect(g, a, 2) → I
  13. Circle(I, HC) → h
  14. Intersect(h, a, 2) → J
  15. OrthogonalLine(G, b) → i
  16. OrthogonalLine(F, b) → j
  17. OrthogonalLine(D, b) → k
  18. OrthogonalLine(H, a) → l
  19. OrthogonalLine(I, a) → m
  20. OrthogonalLine(J, a) → n
  21. Intersect(i, l) → K
  22. Intersect(m, i) → L
  23. Intersect(i, n) → M
  24. Intersect(j, l) → N
  25. Intersect(j, m) → O
  26. Intersect(j, n) → P
  27. Intersect(k, l) → Q
  28. Intersect(k, m) → R
  29. Intersect(k, n) → S
  30. Polygon(A, D, Q, H) → VAxHA, a_1, d_1, q, h_1
  31. Polygon(Q, R, I, H) → VAxHB, q_1, r, i_1, h_2
  32. Polygon(R, S, J, I) → VAxHC, r_1, s, j_1, i_2
  33. Polygon(D, F, N, Q) → VBxHA, d_2, f_1, n_1, q_2
  34. Polygon(N, O, R, Q) → VBxHB, n_2, o, r_2, q_3
  35. Polygon(O, P, S, R) → VBxHC, o_1, p, s_1, r_3
  36. Polygon(G, K, N, F) → VCxHA, g_1, k_1, n_3, f_2
  37. Polygon(K, L, O, N) → VCxHB, k_2, l_1, o_2, n_4
  38. Polygon(L, M, P, O) → VCxHC, l_2, m_1, p_1, o_3
  39. PointIn(VCxHC) → Pointpoly9
  40. PointIn(VCxHA) → Pointpoly7
  41. PointIn(VCxHB) → Pointpoly8
  42. PointIn(VBxHA) → Pointpoly4
  43. PointIn(VBxHB) → Pointpoly5
  44. PointIn(VBxHC) → Pointpoly6
  45. PointIn(VAxHA) → Pointpoly1
  46. PointIn(VAxHB) → Pointpoly2
  47. PointIn(VAxHC) → Pointpoly3