Identify the property or rule that justifies each step in the calculation.

6b+(8b+7c)-9c ____________________
(6b+8b)+(7c-9c)_____________________
(6b+8)b+(7-9)c ____________________

Correction on the last property:

(6+8)b+(7-9)c

To identify the property or rule that justifies each step in the calculation, let's break down the given expressions one by one:

1. 6b + (8b + 7c) - 9c
We start with the expression 6b and then add the grouped expression (8b + 7c). This is done using the Associative Property of Addition because we can rearrange the terms within parentheses without changing the overall value.
Then, we subtract 9c. This is a simple subtraction.

2. (6b + 8b) + (7c - 9c)
Here, we can combine similar terms within parentheses using the Associative Property of Addition. So, 6b and 8b can be added to get 14b, and 7c and -9c can be combined to get -2c.

3. (6b + 8b)b + (7 - 9)c
In this expression, we have a term (6b + 8b) multiplied by b using the Distributive Property. The Distributive Property states that when a number or term is multiplied by the sum or difference of other terms, it can be distributed or applied to each term separately. So, we distribute the b to both 6b and 8b, resulting in 6b^2 + 8b^2.
Similarly, (7 - 9)c simplifies to -2c using simple subtraction.

To summarize:
- Step 1: Associative Property of Addition
- Step 2: Associative Property of Addition
- Step 3: Distributive Property