An odd number is (2x) + 1
An even number is (2x)
These are the definitions.
Using the binomial (2x + 1)(2x + 1), we can see the properties of all products made from odd numbers.
Foiling will give 4x^2 + 4x + 1.
4x^2 is even because 4x^2 can be expressed as 2(2x) x 2(2x).
4x is even because 4x can be expressed as 2(2x)
This means that 4x^2 + 4x is even so the expression 4x^2 + 4x + 1 is odd because an even number + 1 is odd as shown by (2x) + 1.
This shows that every outcome of the product of 2 odd numbers will result being odd.
This means there is no answer to this problem, because any number that is a multiple of 2 is even. (Basically the definition of even)
