Prove for all natural numbers n if n is odd then n^2 + 3n is even

An odd number can be written in the form 2x+1.

(2x+1) (2x+1) + 3 (2x+1) =

4x²+4x+1+6x+3=

4x² + 10x + 4

now 4x² is even because 4 is a multiple of 2

10x is even because 10 is a multiple of 2

4 is even

add 3 evens together and you get yet another even