Square of Difference - Geometrical Explanation - STD 8
📐 Visual Proof: (a-b)² = a² + b² - 2ab
4 Blue Rectangles arranged around a Yellow Central Square
\[
(a - b)^2 = a^2 + b^2 - 2ab
\]
R1: Horizontal Rectangle (a×b)
R2: Vertical Rectangle (a×b) at right of R1
R3: Vertical Rectangle (a×b) left upper of R1
R4: Horizontal Rectangle (a×b) on top of R2
Central Square = (a-b)²
📏 Geometric Representation
\[ \text{Large Square Area} = (a+b)^2 = (a-b)^2 + 4ab \]
\[ \therefore (a-b)^2 = (a+b)^2 - 4ab = a^2 + 2ab + b^2 - 4ab = a^2 - 2ab + b^2 \]
∴ (a-b)² = a² + b² - 2ab
💡 How it works: Four rectangles (each a×b) are arranged around a central square of side |a-b|. The whole figure forms a larger square of side (a+b). So (a+b)² = (a-b)² + 4ab.