Question

How to prove geometrically that : (a+b)²=a²+2ab+b²?

Answer 1

Answer:

Step 1: Draw a square ACDF with AC=a units.

Step 2: Cut AB=b units so that BC=(a−b) unts.

Step 3: Complete the squares and rectangle as shown in the diagram.

Step 4: Area of yellow square IDEO= Area of square ACDF− Area of rectangle GOFE− Area of rectangle BCIO− Area of red square ABOG

Therefore, (a−b)2=a2−b(a−b)−b(a−b)−b2

= a2−ab+b2−ab+b2−b2 

= a2−2ab+b2 

Hence, geometrically we proved the identity (a−b)2=a2−2ab+b