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21-09-2022
Mathematics

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prove that the sum of the squares of two consecutive even numbers is a multiple of 4

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mathstudent55 mathstudent55

21-09-2022

Answer:

Since the final answer has a factor of 4, it is a multiple of 4.

Step-by-step explanation:

Let the smaller even number be 2n.

The next greater even number is 2n + 2.

(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)

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