Prove that the difference between between squares of consecutive even number is always a multiple of 4. Let n stand for any integer in your working.

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Mathematics

Seth

27 April, 19:50

Prove that the difference between between squares of consecutive even number is always a multiple of 4. Let n stand for any integer in your working.

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Gemma Tate · Answer 1

2n and 2n+2 are two consecutive even numbers, then the difference of their squares is:

(2n+2) ² - (2n) ² = (2n+2+2n) (2n+2-2n) = (4n+2) * 2 = 2 * (2n+1) * 2 = 4 * (2n+1)

As we see it is multiple of 4.