Identities in algebra can sometimes be shown as area relationships. Draw figures corresponding to the identities (a + b)(a − b) = a² − b² and (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Question

TextGeometric Visualisation of Algebraic Identities Using Area Models

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A square of side (a + b) is divided into four parts as shown. The figure is a geometric model of the identity

A square of side b is removed from a corner of a square of side a, as shown. The area of the shaded region can be written as