Prove algebraically that: (2n^2 +1)^2 -(2n+1)

Hello from MrBillDoesMath

See below

Discussion:

Note the Question incorrectly shows (2n^2 +1) ^ 2. It should be (2n + 1) ^2.

So

(2 n + 1) ^2 - (2n +1) =  

4n^2 + 4n + 1 - 2n - 1 =                 ( -1 + 1 = 0)

4n^2 + 4n -2n + (1-1)  =

4(X)  = 2 (2X)

Key point. The end result of the evaluation is a multiple of 2 so the result is an even integer.

Thank you,

Mr. B

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right