Fill in the blank
The product of two negative integers and the product of two positive integers is a ______ integer

Hint: Here the question is related to the integers. We have to fill in the blank in the given question. First we know the definition of the integers and about the positive, negative integers. So we consider the table of multiplication of integers and then we can find the blank word.

Complete step-by-step answer:
In mathematics we have different kinds of numbers namely, natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.
The integers are defined as the combination of positive and negative natural numbers along with the number zero.
In a number line we write the integers. Because the number line contains both positive and negative numbers.
The integers are usually represented by I.
Initially we should know the table of multiplication of integers.
\[
   + \times + = + \\
   + \times - = - \\
   - \times + = - \\
   - \times - = + \;
 \]
On considering the table now we solve the given question and fill the blank
The product of two negative integers is a positive and the product of two positive integers is a positive integer which is mentioned in the above table.
Hence the product of two negatives and the product of two positive integers is a positive integer.
Hence the solution.
So, the correct answer is “positive integer.”.

Note: For the two integers we follow the table of multiplication of integers. Suppose if we have a product of more than two integers we follow the property that the product of an old number of negative integers is negative and the product of an even number of negative integers is a positive.