Final answer:
The product of an even integer and any other integer is always even, while the product of two odd integers is always odd.
Step-by-step explanation:
The product of an even integer and any other integer is always even. This can be understood by considering the definition of an even number, which is a number that is divisible by 2. When we multiply an even number by any integer, we are multiplying a number that is divisible by 2 by another number, which means the result will also be divisible by 2 and hence, even. For example, 2 × 3 = 6, 4 × (-5) = -20, and so on.
On the other hand, the product of two odd integers is always odd. This can be understood by considering the definition of an odd number, which is a number that is not divisible by 2. When we multiply two odd numbers, we are multiplying two numbers that are not divisible by 2, and no matter the result, it will not be divisible by 2 either. For example, 3 × (-7) = -21, (-5) × 9 = -45, and so on.