Prove using algebra that the difference between the squares of consecutive odd numbers is always a multiple of 8.

See  below

Step-by-step explanation:

Lets label the consecutive odd numbers as 2n+1 and 2n+3 where n is an integer.

We need to prove that

((2n + 3)^2 - (2n + 1)^2 is a multiple of 8.

Using the difference of 2 squares on the left side:-

(2n + 3 + 2n + 1)(2n + 3 -  (2n + 1)

=  (4n + 4)(2)

= 8n + 8  which is a multiple of 8