Prove algebraically that (n + 3)(2n + 1) + (n - 2)(2n + 1) is not an even number

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.

idc

step-by-step explanation:

idk

what "following statement"?

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