Question

prove that the difference of the square of an even number is a multiple of 4

Answer 1

Answer: very even number is in the form of 2x.

Let the consecutive even number be 2(x+1).

Now, the square of even number would be = 2x * 2x = 4x

and consecutive number would be 2(x+1)*2(x+1) = 4(x+1)(x+1)

On, adding the square we get,

4x + 4(x+1)(x+1) = 4(x+(x+1)(x+1))= 4(x^2 + 3x + 1), and this is divisible by 4

Answer 2

Step-by-step explanation:

1. take any two even number squares. (in my case: 2 and 4)

2. Square them up. (in my proving, 2^2=4, 4^4=16).

3. Subtract them. (in mine, 16-4=12 which is a multiple of 4).

4. Hence Verified..

hope u have understood dear.