Question

N is an integer. Prove that (2n+1)(n+3)+(2n+1)(n-2) is not a multiple of 2. thanks.

Answer 1

(2n + 1)(n + 3) + (2n + 1)(n - 2)

= (2n + 1)(n + 3 + n - 2)

= (2n + 1)2n + 1)

= 4n² + 4n + 1

= 2(2n² + 2n) + 1

can see 2(2n² + 2n) is a multiple of 2 but 1 isnt a multiple of 2

=> 2(2n² + 2n) + 1 is not a multiple of 2

=> (2n + 1)(n + 3) + (2n + 1)(n - 2) is not a multiple of 2

Explanation: