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OverLord2011 [107]
3 years ago
10

Show that (n+3)2 - (n-3)2 is an even number for all positive interger values of n

Mathematics
2 answers:
Zolol [24]3 years ago
7 0
(n+3)^2-(n-3)^2=\\
n^2+6n+9-(n^2-6n+9)=\\
n^2+6n+9-n^2+6n-9=\\
12n
Dmitriy789 [7]3 years ago
3 0
As both parts of the expression are multiplied by two, Both parts will be even numbers. When subtracting an even number from an even number the answer will always be even.

Example: let n=1 (odd number)

(1+3)2- (1-3)2

4*2-(-2)2

8-(-4)

8+4

12

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