What is the product of two odd numbers and a multiple of 2

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)

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