Observe the two rows of figures below. They represent an algebraic identity. Try to identify it. Class 9

Observe the two rows of figures below. They represent an algebraic identity. Try to identify it. Class 9

Question 1.

Observe the two rows of figures below. They represent an algebraic identity. Try to identify it. Class 9

Answer:

In the top row, the squares have side lengths:

a + b + c, a + b - c, a - b + c, a - b - c

So, total area of the top row is

(a + b + c)² + (a + b - c)² + (a - b + c)² + (a - b - c)²

= (a² + b² + c² + 2ab + 2ac + 2bc) + (a² + b² + c² + 2ab - 2ac - 2bc) + (a² + b² + c² - 2ab + 2ac - 2bc) + (a² + b² + c² - 2ab - 2ac + 2bc)

= 4a² + 4b² + 4c²

In the bottom row, the squares have side lengths: 2a, 2b, 2c

So, total area of the bottom row is

(2a)² + (2b)² + (2c)² = 4a² + 4b² + 4c²

Since the total areas of both rows are equal, the figures represent the identity:

(a + b + c)² + (a + b - c)² + (a - b + c)² + (a - b - c)² = 4(a² + b² + c²)