Question

Prove that two odd numbers multiply to an odd number.

a) Odd
b) Even
c) Prime
d) Composite

Answer 1

To prove that two odd numbers multiply to an odd number, we can use the distributive property and expand the expression to show that the product is always odd.

Step-by-step explanation:

1. Let the two odd numbers be represented as 2n+1 and 2m+1, where n and m are integers.
2. The product of the two odd numbers is (2n+1)(2m+1).
3. Using the distributive property, we can expand the expression: (2n+1)(2m+1) = 4nm + 2n + 2m + 1.
4. Notice that all the terms in the expanded expression are either even except for the constant term 1, which is odd.
5. Therefore, the product of two odd numbers is always odd.