Prove algebraically that the difference of the squares of any two consecutive even numbers are always a multiple of 4

Guest Mar 3, 2021

#1**0 **

An even number has a factor of 2, so we can represent it as 2x.

The other number will be 2x + 2.

So we're tryign to prove that

(2x+2)^2-(2x)^2 = multiple of 4

4x^2+8x+4-4x^2

8x+4

4(2x+1).

The number has to have a factor of 4, making it a multiple of 4.

I hope this helped. :)))

=^._.^=

catmg Mar 3, 2021