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Expanding and Factorising

Expanding and Factorising
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2013-09-02 15:04
FunctionTransformationGeometric ConstructionSlider Animation
This example visually demonstrates the concepts of expanding and factorising polynomials. It shows the process of transforming algebraic expressions, helping students understand the manipulation of expressions. Utilizes commands like Polygon and Textfield in GeoGebra, suitable for middle and high school math education.

GeoGebra Commands & Parameters

  1. Polygon((1, 1), (1, 1 + v * n_1), (1 + h * n_1, 1 + v * n_1), (1 + h * n_1, 1)) → poly1, a, b, c, d
  2. Polygon((1 + h * n_1, 1), (1 + h * n_1 + C_h, 1), (1 + h * n_1 + C_h, 1 - C_v), (1 + h * n_1, 1 - C_v)) → poly2, e, f, g, i
  3. Polygon((1, 1 - C_v), (1, 1 + v * n_1), (1 + h * n_1 + C_h, 1 + v * n_1), (1 + h * n_1 + C_h, 1 - C_v)) → poly3, j, k, l, m
  4. Textfield(C_v) → constant_ height
  5. Textfield(C_h) → constant_ width
  6. Textfield(h) → Width_ multiplier
  7. Textfield(v) → Height_ multiplier
  8. Textfield(n_1) → n
  9. Textfield(C_v) → Height_ 1variable
  10. Textfield(C_h) → Width_ 1variable
  11. Polygon((1, 1), (1, 1 + C_v), (1 + h * n_1 + C_h, 1 + C_v), (1 + h * n_1 + C_h, 1)) → poly3A, p, q, r, s
  12. Polygon((1, 1), (1, 1 + C_v), (1 + h * n_1, 1 + C_v), (1 + h * n_1, 1)) → poly1A, t, a_1, b_1, c_1
  13. Polygon((1 + h * n_1, 1), (1 + h * n_1, 1 + C_v), (1 + h * n_1 + C_h, 1 + C_v), (1 + h * n_1 + C_h, 1)) → poly2B, d_1, e_1, f_1, g_1

AI Drawing Prompt Reference

Draw a rectangle with initial height 1 and width 1. Use sliders to adjust the height and width ratios. Then draw two new rectangles, one to the right of the original and one above it. Change the size of the rectangles by adjusting the sliders and observe how the rectangles are expanded and factored through addition and multiplication operations.
The prompt above was compiled from the original drawing commands and is for reference only.