Question

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

Answer 1

$(n+3)^2-(n-3)^2=\\ n^2+6n+9-(n^2-6n+9)=\\ n^2+6n+9-n^2+6n-9=\\ 12n$

Answer 2

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