Final answer:
The expression |ab| simplifies to -ab if a is negative and b is positive. The expression |2b| without the absolute value sign is -2b if b is negative, reflecting the sign rules of multiplication.
Step-by-step explanation:
To simplify the expression |ab| where a is less than 0 and b is greater than 0, we need to understand the properties of multiplication concerning signs. Given by the rule, when a positive number multiplies a negative number, the result is negative. Therefore, |ab| is the absolute value of a negative number, which will be a positive number that is equal in magnitude to the product of a and b but without the sign. So, |ab| simplifies to -ab because a is negative and b is positive.
When writing without the absolute value sign for |2b| where b is less than 0, we consider that 2b is negative since it is the product of a positive number (2) and a negative number (b). Thus, the expression |2b| equates to -2b. The absolute value sign makes the negative product positive, but without the absolute value sign, the expression remains -2b.