The difference between the squares of two consecutive whole numbers is equal to?

Answer 1

Let's name the first number x and the next number x + 1. So,

x^2 - (x + 1)^2

= x^2 - (x^2 + 2x + 1)

= x^2 - x^2 - 2x - 1

= - 2x - 1

= -(2x + 1)

Thus we can say that, the difference between the squares of two consecutive numbers is equal to the opposite of their sum (means it is their sum, but as a negative number).

Let's do some examples:

2, 3; 2 + 3 = 5

2^2 - 3^2 = 4 - 9 = -5 ( 5 and -5 are opposite numbers, and 5 is the sum of 2 and 3)

13, 14; 13 + 14 = 27

13^2 - 14^2 = 169 - 196 = -27 (27 and -27 are opposite numbers, and 27 is the sum of 13 and 14)