Question

Find the square using (a+b)²=a²+2ab+b² identify. A)72

Answer 1

Step-by-step explanation:

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

=a

2

−b(a−b)−b(a−b)−b

2

= a

2

−ab+b

2

−ab+b

2

−b

2

= a

2

−2ab+b

2

Hence, geometrically we proved the identity (a−b)

2

=a

2

−2ab+b

2

.