Relationship between Algebra and Geometry

It is interesting to represent Algebraic Identities using Geometric objects. In other words the Relationship between algebra and geometry.  One easy example is presented in this video.

Think! Relationship between Algebra and Geometry 

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Try to draw the following algebraic identities using geometric objects

• \(a^2 - b^2 = (a+b)(a-b) \)
• \( (a+b)^3 = a^3 + 3a^2 b + 3 ab^2 + b^3 \)
• \( 1 + 2 + ... + n = \frac {n(n+1)}{2} \)