分配律的面积可视化：矩形分割与代数等价

① This example visually demonstrates the distributive property a(b+c)=ab+ac by partitioning a rectangle into two smaller rectangles, showing that the total area equals the sum of the sub-areas. ② The core mathematical concept is the distributive property and its area model, linking algebraic manipulation to geometric area. ③ Construction details: using GeoGebra commands such as Point, Segment, Line, Polygon, Distance, and Intersect to create the rectangle, its partition line, and measure side lengths; objects include points (A, B, C, D, etc.), segments (a, b, c, etc.), polygons (poly1, poly2, etc.), and auxiliary lines, forming an interactive area decomposition. ④ Suitable for middle school mathematics, helping students grasp the geometric meaning of the distributive law, and useful for classroom demonstrations or self-study.