Question

if two odd numbers are multiplied together, is the product an even number or an odd number?

choose the correct answer.

a. the product of two odd numbers is an even number.

b. the product of two odd numbers is an odd number.

Explanation:

Step1: Define odd numbers

Any odd number can be written as $2k+1$ where $k$ is an integer. Let the two odd numbers be $2m+1$ and $2n+1$, where $m,n$ are integers.

Step2: Multiply the two numbers

$$(2m+1)(2n+1) = 4mn + 2m + 2n + 1$$

Step3: Simplify the expression

Factor out 2 from the first three terms:
$$= 2(2mn + m + n) + 1$$
Let $p=2mn+m+n$, where $p$ is an integer. The expression becomes $2p+1$, which fits the form of an odd number.

Answer:

B. The product of two odd numbers is an odd number.