The difference of squares of two consecutive odd numbers is always

Let the two consecutive odd numbers be represented as (2n - 1) and (2n + 1), where n is an integer. To find the difference of their squares, we calculate:

(2n + 1)² - (2n - 1)²

Using the algebraic identity a² - b² = (a - b)(a + b):

• a = 2n + 1
• b = 2n - 1
• (a - b) = (2n + 1) - (2n - 1) = 2
• (a + b) = (2n + 1) + (2n - 1) = 4n

The difference is 2 × 4n = 8n. Since n is an integer, the result 8n is always a multiple of 8, meaning it is always divisible by 8. For example, 3² - 1² = 8 and 5² - 3² = 16; both are divisible by 8. However, since 8 is not divisible by 16 or 3, those options are not universally true.