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

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. :)))

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