-3 (a + b) + 4 (2a - 3b) - (2a - b)

Options

A. 3a - 15 b
B. 3a -14b
C. 4a - 12 b
D. 5b - 6 a

Answer

To solve the expression \(-3 (a + b) + 4 (2a - 3b) - (2a - b)\), we will follow these steps:

### Step 1: Distribute the terms inside the brackets
We will start by distributing the coefficients outside the brackets to the terms inside:

1. For \(-3(a + b)\):
\[ -3 \cdot a - 3 \cdot b = -3a - 3b \]

2. For \(4(2a - 3b)\):
\[ 4 \cdot 2a + 4 \cdot (-3b) = 8a - 12b \]

3. For \(-(2a - b)\):
\[ -1 \cdot 2a + 1 \cdot b = -2a + b \]

Now, we can rewrite the expression by substituting these results back in:
\[ -3a - 3b + 8a - 12b - 2a + b \]

### Step 2: Combine like terms
Now we will combine the like terms (the terms with \(a\) and the terms with \(b\)):

1. Combine the \(a\) terms:
\[ -3a + 8a - 2a = (8 - 3 - 2)a = 3a \]

2. Combine the \(b\) terms:
\[ -3b - 12b + b = (-3 - 12 + 1)b = -14b \]

### Step 3: Write the final expression
Putting it all together, we have:
\[ 3a - 14b \]

Thus, the final simplified expression is:
\[ \boxed{3a - 14b} \]

---