Question

Simplify the expression |ab| if a<0 and b>0

Answer 1

Answer:

$|ab|=-ab\\|2b|=-2b\\|c|=-c$

Step-by-step explanation:

Given:

The expressions to simplify are:

1. $|ab|\ if\ a0$

We know that, product of a negative number and a positive number is always negative.

Here, 'a' is less than 0 or a negative number. 'b' is greater than 0 or a positive number. The product of 'a' and 'b' is a number less than 0 or a negative number. Now, we need to find the absolute value of their product. The absolute value is never negative. So, in order to make the product positive, we multiply the product by -1 as product of two negative numbers is always positive.

Therefore, $|ab|=-1\times ab=-ab$

2. $|2b|\ if\ b$

Here, also, 'b' is less than 0 or a negative number. Therefore, the number '2b' is a negative number So, in order to write this without the absolute value sign, we have to multiply '2b' by -1 to make the product always positive.

Therefore, $|2b|=-1\times b = -2b$

3. $|c|\ if\ c$

This is also similar to the one above. Since 'c' is a negative number, we need to multiply it by -1 when we remove the absolute value sign.

Thus, $|c|=-1\times c=-c$