Prove using algebra that the difference between the squares of consecutive odd numbers is always a multiple of 8.

Let 2n+1 be the smaller of the two odd numbers.

Question

Amelia Vaughan

9 April, 12:45

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Answers (1)

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Waylon Rivera · Answer 1

in steps

Step-by-step explanation:

(2n+3) ² - (2n+1) ² = 4n² + 12n + 9 - 4n² - 4n - 1

= 8n + 8 = 8 (n + 1) ... always multiple of 8

Prove using algebra that the difference between the squares of consecutive odd numbers is always a multiple of 8.Let 2n+1 be the smaller of the two odd numbers.