Question

Prove that the difference between squares of consecutive even numbers is always a multiple of 4

Answer 1

Answer:

let's take 2 and 4 as our examples

then the difference between the squares is

4^2-2^2

=16-4

=12

so 12 is even number

the consecutive even number is always a square of mulitiple of 4 mark as brainliesht

Answer 2

the 1st even no. would be= 2n

let the next consecutive even no. = 2(n+1)

the squares of each consecutive even no. would be= (2n)²= 2n× 2n= 4n²

= {2(n+1)}²= (2n+2)² = (2n+2)(2n+2)

expanding the brackets

=4n²+4n+4n+4

{2(n+1)}²=4n²+8n+3