Answer :
Certainly! Let's analyze Mark's work and then correct the mistake he made.
### Mark's Work:
Mark attempted to simplify:
[tex]\[ (-3)(-5)(-2) \][/tex]
He performed the multiplication in steps:
1. First, he multiplied [tex]\( -3 \)[/tex] and [tex]\( -5 \)[/tex]:
[tex]\[ (-3) \times (-5) = 15 \][/tex]
2. Next, he multiplied the result by [tex]\( -2 \)[/tex]:
[tex]\[ 15 \times (-2) \][/tex]
However, he made an error in the second multiplication. Mark incorrectly stated:
[tex]\[ (-15) \times (-2) = 30 \][/tex]
### Explanation of the Error:
In the second step, Mark mistakenly treated the intermediate result [tex]\( 15 \)[/tex] as [tex]\( -15 \)[/tex], and incorrectly applied the rules of multiplication.
### Correct Approach:
To find the correct product, follow these steps step by step properly:
#### Step 1: Multiply the first two numbers.
[tex]\[ (-3) \times (-5) = 15 \][/tex]
When multiplying two negative numbers, the result is positive.
#### Step 2: Multiply the intermediate result by the third number.
[tex]\[ 15 \times (-2) \][/tex]
When multiplying a positive number with a negative number, the result is negative.
[tex]\[ 15 \times (-2) = -30 \][/tex]
### Conclusion:
The correct simplification and product are given by:
[tex]\[ (-3)(-5)(-2) = 15 \times (-2) = -30 \][/tex]
Therefore, the correct product is:
[tex]\[ -30 \][/tex]
### Mark's Work:
Mark attempted to simplify:
[tex]\[ (-3)(-5)(-2) \][/tex]
He performed the multiplication in steps:
1. First, he multiplied [tex]\( -3 \)[/tex] and [tex]\( -5 \)[/tex]:
[tex]\[ (-3) \times (-5) = 15 \][/tex]
2. Next, he multiplied the result by [tex]\( -2 \)[/tex]:
[tex]\[ 15 \times (-2) \][/tex]
However, he made an error in the second multiplication. Mark incorrectly stated:
[tex]\[ (-15) \times (-2) = 30 \][/tex]
### Explanation of the Error:
In the second step, Mark mistakenly treated the intermediate result [tex]\( 15 \)[/tex] as [tex]\( -15 \)[/tex], and incorrectly applied the rules of multiplication.
### Correct Approach:
To find the correct product, follow these steps step by step properly:
#### Step 1: Multiply the first two numbers.
[tex]\[ (-3) \times (-5) = 15 \][/tex]
When multiplying two negative numbers, the result is positive.
#### Step 2: Multiply the intermediate result by the third number.
[tex]\[ 15 \times (-2) \][/tex]
When multiplying a positive number with a negative number, the result is negative.
[tex]\[ 15 \times (-2) = -30 \][/tex]
### Conclusion:
The correct simplification and product are given by:
[tex]\[ (-3)(-5)(-2) = 15 \times (-2) = -30 \][/tex]
Therefore, the correct product is:
[tex]\[ -30 \][/tex]
