15-01-2020
Mathematics

contestada

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.

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kenlingdad kenlingdad

15-01-2020

Answer:

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

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