Question

Is the product of any two odd integers also odd?

A) Yes
B) No
C) Sometimes
D) Undefined

Answer 1

Yes, the product of any two odd integers is always odd.

Step-by-step explanation:

Yes, the product of any two odd integers is always odd. To understand why, let's consider two odd integers, represented by the values n and m. An odd number can be expressed as 2k+1, where k is an integer. Therefore, n = 2a+1 and m = 2b+1, where a and b are integers. When we multiply these two odd integers, we get:

n × m = (2a+1) × (2b+1)

n × m = 4ab + 2a + 2b + 1

n × m = 2(2ab + a + b) + 1

As you can see, the product of the two odd integers is in the form 2k+1, which is the representation of an odd number. Therefore, the product of any two odd integers is always odd.