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FOIL Expansion of (a+b)² Demonstration

FOIL Expansion of (a+b)² Demonstration
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2012-10-03 06:42
PolygonCoordinate GeometryGeometric Construction
In collections Geo&Alg:Area Volume Pythagorean Th.
This GeoGebra applet visually demonstrates the FOIL expansion of the binomial square (a+b)², showing how (a+b)(a+b) equals a² + 2ab + b² through an area model. Core mathematical concepts include the binomial square formula, the distributive law, and the geometric interpretation of algebraic expressions. Construction highlights: the applet uses GeoGebra commands Point, Segment, Polygon, Circle, Intersect, OrthogonalLine, and Text to create points A, B, C, D, E, F, G, H, I, J, K and polygons poly1, poly2, poly3, together with algebraic objects aXa, bXb, aXb, cXc representing a², b², and ab terms. It is suitable for middle‑school algebra‑geometry integration, high‑school algebra review, and teacher‑created instructional materials.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a_1 + b_1]) → B
  2. Segment(A, B) → c_1
  3. Polygon(A, B, 4) → poly1, a_4, b_4, d, e, C, D
  4. Circle(D, a_1) → f
  5. Circle(B, b_1) → g
  6. Intersect(f, d) → E,
  7. Intersect(f, e) → F,
  8. Intersect(g, b_4) → G,
  9. Intersect(g, c_1) → H,
  10. OrthogonalLine(E, d) → h
  11. OrthogonalLine(F, e) → i
  12. Intersect(i, h) → I
  13. Segment(F, H) → c
  14. Polygon(D, F, I, E) → poly2, a_3, a, i_1, e_1
  15. Polygon(I, H, B, G) → poly3, b, h_1, b_2, g_1
  16. Point(Circle[J, a_1 + b_1]) → K
  17. Circle(J, a_1) → p
  18. Circle(J, b_1) → r
  19. Text(aXa) → text1
  20. Text(bXb) → text2
  21. Text(aXb) → text3
  22. Text(cXc) → text4
  23. Text(c) → text5