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Multiplying Binomial Expressions Geometrically

Multiplying Binomial Expressions Geometrically
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2016-09-19 19:35
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the process of multiplying binomials geometrically. Key mathematical concepts include polynomial multiplication and geometric representation. Using GeoGebra commands such as Segment, RandomElement, and Polynomial, the process of multiplication is dynamically shown. Suitable for students in middle school and above to learn polynomial multiplication and geometric representation.

GeoGebra Commands & Parameters

  1. Segment(A, C) → f
  2. Segment(A, F) → g
  3. Segment(F, H) → h
  4. Segment(C, H) → i
  5. Segment(B, G) → j
  6. Segment(D, E) → k
  7. RandomElement(list1) → m
  8. RandomElement(list2) → n
  9. RandomElement(list3) → u
  10. RandomElement(list4) → v
  11. Polynomial((m * x) + u) → p
  12. Polynomial((n * x) + v) → q
  13. Polynomial((p(x) * q(x))) → r
  14. Polynomial(((m * x) * (n * x))) → s
  15. Polynomial(((n * x) * u)) → t
  16. Polynomial(((m * x) * v)) → f_1
  17. Polynomial((u * v)) → g_1
  18. Polynomial(((m + n) * x^(2))) → h_1
  19. Polynomial(((m + v) * x)) → p_1
  20. Polynomial(((n + u) * x)) → q_1
  21. Polynomial(u + v) → r_1
  22. Polynomial(((m * n) * x)) → s_1
  23. Intersect(g, h) → I
  24. Intersect(h, j) → J
  25. Intersect(j, k) → K
  26. Intersect(g, k) → L
  27. Distance(I, J) → distanceIJ
  28. Point(Circle[M, 2]) → N
  29. Segment(M, N) → l
  30. OrthogonalLine(M, l) → b
  31. OrthogonalLine(N, l) → c
  32. Distance(M, b) → distanceMb
  33. Point(Circle[M, 2]) → O
  34. Segment(M, O) → d
  35. Rotate(M, 270°, M) → M'
  36. Rotate(O, 270°, M) → O'
  37. Segment(M', O') → d'
  38. OrthogonalLine(O', d') → e
  39. Intersect(c, e) → P
  40. Polygon(M, N, P, O') → poly1, m_1, n_1, p_2, o'
  41. Distance(M, N) → distanceMN
  42. Point(Circle[Q, 2]) → R
  43. Segment(Q, R) → i_1
  44. Rotate(Q, 270°, Q) → Q'
  45. Rotate(R, 270°, Q) → R'
  46. Segment(Q', R') → j_1
  47. OrthogonalLine(R', j_1) → k_1
  48. OrthogonalLine(R, i_1) → l_1
  49. Intersect(k_1, l_1) → S
  50. Polygon(Q, R, S, R') → poly2, q_2, r_2, s_2, r'
  51. Distance(Q, R) → distanceQR
  52. Point(Circle[T, 2]) → U
  53. Segment(T, U) → t_1
  54. Rotate(T, 270°, T) → T'
  55. Rotate(U, 270°, T) → U'
  56. Segment(T', U') → c_8
  57. OrthogonalLine(U', c_8) → e_1
  58. OrthogonalLine(U, t_1) → f_2
  59. Intersect(e_1, f_2) → V
  60. Polygon(T, U, V, U') → poly3, t_2, u_1, v_1, u'
  61. Distance(T, U) → distanceTU
  62. Point(Circle[W, 2]) → Z
  63. Segment(W, Z) → g_2
  64. Rotate(W, 270°, W) → W'
  65. Rotate(Z, 270°, W) → Z'
  66. Segment(W', Z') → h_2
  67. OrthogonalLine(Z', h_2) → i_2
  68. OrthogonalLine(Z, g_2) → j_2
  69. Intersect(i_2, j_2) → A_1
  70. Polygon(W, Z, A_1, Z') → poly4, w, z_1, a_3, z'
  71. Distance(W, Z) → distanceWZ
  72. Point(Circle[B_1, 2]) → C_1
  73. Segment(B_1, C_1) → k_2
  74. Rotate(B_1, 270°, B_1) → D_1
  75. Rotate(C_1, 270°, B_1) → E_1
  76. Segment(D_1, E_1) → l_2
  77. OrthogonalLine(E_1, l_2) → m_2
  78. OrthogonalLine(C_1, k_2) → n_2
  79. Intersect(m_2, n_2) → F_1
  80. Polygon(B_1, C_1, F_1, E_1) → poly5, b_3, c_2, f_3, e_2
  81. Distance(B_1, C_1) → distanceB1C1
  82. Point(Circle[G_1, 2]) → H_1
  83. Segment(G_1, H_1) → g_3
  84. Rotate(G_1, 270°, G_1) → I_1
  85. Rotate(H_1, 270°, G_1) → J_1
  86. Segment(I_1, J_1) → h_3
  87. OrthogonalLine(J_1, h_3) → i_3
  88. OrthogonalLine(H_1, g_3) → j_3
  89. Intersect(i_3, j_3) → K_1
  90. Polygon(G_1, H_1, K_1, J_1) → poly6, g_4, h_4, k_3, j_4
  91. Distance(G_1, H_1) → distanceG1H1
  92. Point(Circle[L_1, 2]) → M_1
  93. Segment(L_1, M_1) → l_3
  94. Rotate(L_1, 270°, L_1) → N_1
  95. Rotate(M_1, 270°, L_1) → O_1
  96. Segment(N_1, O_1) → m_3
  97. OrthogonalLine(O_1, m_3) → n_3
  98. OrthogonalLine(M_1, l_3) → p_3
  99. Intersect(n_3, p_3) → P_1
  100. Polygon(L_1, M_1, P_1, O_1) → poly7, l_4, m_4, p_4, o_1
  101. Distance(L_1, M_1) → distanceL1M1
  102. Point(Circle[Q_1, 2]) → R_1
  103. Segment(Q_1, R_1) → q_3
  104. Rotate(Q_1, 270°, Q_1) → S_1
  105. Rotate(R_1, 270°, Q_1) → T_1
  106. Segment(S_1, T_1) → r_3
  107. OrthogonalLine(T_1, r_3) → s_3
  108. OrthogonalLine(R_1, q_3) → t_3
  109. Intersect(s_3, t_3) → U_1
  110. Polygon(Q_1, R_1, U_1, T_1) → poly8, q_4, r_4, u_2, t_4
  111. Distance(Q_1, R_1) → distanceQ1R1
  112. Point(Circle[V_1, 2]) → W_1
  113. Segment(V_1, W_1) → c_3
  114. Rotate(V_1, 270°, V_1) → Z_1
  115. Rotate(W_1, 270°, V_1) → A_2
  116. Segment(Z_1, A_2) → d_3
  117. OrthogonalLine(A_2, d_3) → e_3
  118. OrthogonalLine(W_1, c_3) → f_4
  119. Intersect(e_3, f_4) → B_2
  120. Polygon(V_1, W_1, B_2, A_2) → poly9, v_2, w_1, b_4, a_4
  121. Distance(V_1, W_1) → distanceV1W1
  122. Polynomial((p(x) * v)) → f_5
  123. Polynomial(((p(x) * n) * x)) → s_4
  124. Polynomial(s_4(x) + f_5(x)) → g_5
  125. Polynomial(((m * x) * q(x))) → h_5
  126. Polynomial((u * q(x))) → p_5
  127. Polynomial(h_5(x) + p_5(x)) → q_5