ALL EXPERIMENTS

Distributive Property

Explore geometric proofs for algebraic identities.

a² a×b b×a b²

Expanding (a+b)²

(a+b)² = a² + 2ab + b²
(60 + 20)² = 60² + 2(60)(20) + 20²
a(a-b) b(a-b)

Identity: a² - b²

a² - b² = (a+b)(a-b)

Sridharacharya's visual method: Remove the square b² from the corner of a², then rearrange the remaining two rectangles to form a single large rectangle!

Visualizing k(k+2)

k × (k+2) = k² + 2k
4 × (4+2) = 4² + 2(4) = 24

A rectangle of width k and height k+2 can be visually split into a k×k square and a 2×k rectangle. This perfectly mirrors the algebraic expansion!