Answer:
The expression simplifies to 8(3n), a multiple of 8.
Explanation:
For integer values of n, you want to prove that (2n + 3)² - (2n - 3)² is a multiple of 8.
Simplify
The given expression is the difference of squares. It can be simplified to the product ...
(2n + 3)²- (2n - 3)² = ((2n + 3) - (2n - 3))×((2n + 3) + (2n - 3))
= (2n +3 -2n +3)(2n +3 +2n -3)
= 6(4n) = 24n = 8(3n)
For any integer n, the given expression will be a multiple of 8.
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Additional comment
It will also be a multiple of 2, 3, 4, 6, 12, and 24, as well as n.