Prove algebraically that the difference of the squares of any two consecutive even numbers are always a multiple of 4
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
The number has to have a factor of 4, making it a multiple of 4.
I hope this helped. :)))