Subtract: [3b - 2c] - [6c + 2b] - [b+c].
To subtract the given expression, we need to simplify each bracketed expression first.
First bracketed expression: [3b - 2c]
Second bracketed expression: [6c + 2b]
Third bracketed expression: [b + c]
Now let's simplify each expression:
First bracketed expression: [3b - 2c] = 3b - 2c
Second bracketed expression: [6c + 2b] = 6c + 2b
Third bracketed expression: [b + c] = b + c
Now we can subtract the simplified expressions:
[3b - 2c] - [6c + 2b] - [b+c] = (3b - 2c) - (6c + 2b) - (b + c)
Using the distributive property, we can remove the brackets:
= 3b - 2c - 6c - 2b - b - c
Now let's combine like terms:
= (3b - 2b) + (-2c - 6c - c) = b - 9c
Therefore, the simplified expression is b - 9c.