Question

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

Answer 1

Hello from MrBillDoesMath

Answer:

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