Question

Prove that the difference between squares of consecutive even numbers is always a multiple of 4. Note: Let n stand for any integer in your working. Total marks: 4

Answer 1

see explanation

Explanation:

consecutive even numbers have a difference of 2

let the consecutive even numbers be n and n + 2, thus

(n + 2)² - n² ← expand (n + 2)² using FOIL

= n² + 4n + 4 - n² ← collect like terms

= 4n + 4

= 4(n + 1) ← which results in a multiple of 4