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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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mhanifa

Answer:

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.

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