Subtract: (3b−2c)−(6c+2b)−(b+c) .(1 point)
To subtract these expressions, we need to distribute the negative sign to each term within the parentheses.
By doing this, we obtain:
(3b - 2c) - (6c + 2b) - (b + c) = 3b - 2c - 6c - 2b - b - c.
Next, we can combine like terms by adding or subtracting the coefficients of the same variable:
3b - 2b - b - 2c - 6c - c = (3b - 2b - b) + (-2c - 6c - c).
This simplifies to:
= 0b - 9c.
Since any term multiplied by 0 is equal to 0, the result is simply:
0 - 9c = -9c.
Therefore, the expression (3b - 2c) - (6c + 2b) - (b + c) is equal to -9c.
To subtract the given expression, we need to combine like terms. Let's break it down step-by-step:
First, distribute the negative sign to each term inside the second parentheses:
(3b - 2c) - (6c + 2b) - (b + c)
= 3b - 2c - 6c - 2b - b - c
Next, combine like terms by adding or subtracting coefficients of the same variables:
= (3b - 2b) + (-2c - 6c - c) - b
= b - 9c - b
= -9c
Therefore, the simplified expression is -9c.
To subtract the expression (3b - 2c) - (6c + 2b) - (b + c), we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Let's break down the expression step-by-step:
Step 1: Simplify the parentheses from left to right.
- First, simplify (6c + 2b) within the second set of parentheses:
(3b - 2c) - (6c + 2b) - (b + c)
= (3b - 2c) - (2b + 6c) - (b + c)
- Then, simplify (b + c) within the third set of parentheses:
= (3b - 2c) - (2b + 6c) - (b + c)
= (3b - 2c) - (2b + 6c - b - c)
= (3b - 2c) - (b + 5c)
Step 2: Apply the subtraction between the parentheses.
- Distribute the negative sign inside the third set of parentheses:
= 3b - 2c - b - 5c
Step 3: Combine like terms.
- Combine the terms that contain "c" together and the terms that contain "b" together:
= (3b - b) + (-2c - 5c)
= 2b - 7c
Therefore, the final expression is 2b - 7c.