Answer:
Step-by-step explanation:
Suppose that (n+3)(2n+1)+(n-2)(2n+1) is not an even number.
Then we simplify the expression (n+3)(2n+1)+(n-2)(2n+1):
2n^2+6n+n+3+2n^2-4n+n-2
2n^2+2n^2+6n+n-4n+n+3-2
4n^2+7n-4n+n+1
4n^2+3n+n+1
4n^2+4n+1.
Note that 4n^2+4n=4n(n+1)=4n(m)=4mn where m=n+1 is even.
Thus 4n^2+4n+1 must be odd.
Therefore, (n+3)(2n+1)+(n-2)(2n+1) is not an even number.
