Final answer:
The expressions are correctly categorized by applying the product rules for signs: both 'a' (-3)(-3) and 'c' (-1)(-1) are Positive because they involve the multiplication of two negative numbers, while 'd' (-19) is simply Negative. Expression 'b' seems to have a typo; if corrected to (-1)(-3), it would also be Positive.
Step-by-step explanation:
The question involves applying the product rule for determining the sign of each expression. Here's the correct categorization based on the rules stated:
- a. (-3)(-3) - According to the rule that says when two negative numbers are multiplied, the result is positive, this expression is Positive.
- b. (-)(−3) - This appears to be a typo, but if it were (-1)(-3), following the same rule as in 'a', it would also be Positive.
- c. (-1)(-1) - Again, since both numbers are negative, this expression is Positive.
- d. (-19) - This expression is just a single negative number without a multiplication, so by default, it is Negative.
Remember that the multiplication of two positive numbers or two negative numbers always results in a positive product, while the multiplication of numbers with differing signs results in a negative product.