The difference of the squares of two consecutive numbers is their sum.

Question

State whether the statements are true (T) or false (F)

The difference of the squares of two consecutive numbers is their sum.

Answer 1

True

Let two consecutive numbers be x and (x + 1).

Then square of these numbers are x² and (x + 1)².

Difference of squares of these consecutive numbers = (x + 1)² – x²

= x² + 1 + 2x – x² [(a + b)² = a² + b² + 2ab)]

= 2x + 1

= x + x + 1

= (x) + (x + 1)

= sum of the two consecutive numbers x and x+1

Thus, difference of squares of two consecutive numbers = sum of the same consecutive numbers.