Algebraic Identities

Explore the spatial and geometric foundations of algebra. Algebraic identities are equations that hold true for all values of their variables. By mapping these identities to areas, we transform abstract symbols into intuitive physical shapes.

Identity Hub

Core Identities

Select an identity below to open its dedicated interactive worksheet. Each sheet includes real-time coordinate solvers, step-by-step arithmetic proofs, and interactive HTML5 Canvas visualizers.

IDENTITY 01 ★

(a + b)² = a² + 2ab + b²

Square of a Sum

Visualize a square partitioned into two smaller squares of area a² and b², and two matching rectangular spaces of area ab.

Open Simulator

IDENTITY 02 ★

(a - b)² = a² - 2ab + b²

Square of a Difference

Understand how subtracting two regions of area ab from a larger square of area a² overlaps at the corner, requiring b² to be added back.

Open Simulator

IDENTITY 03 ★

a² - b² = (a - b)(a + b)

Difference of Squares

Slice an L-shaped region from a square with a cut-out corner, then rotate and rearrange it to form a single rectangle.

Open Simulator