If A = 3a - 2b, B = -2a + 3b and C = - a - b, then find A + B +C.

Answer

To solve the problem, we need to find the sum of the expressions A, B, and C. Let's break it down step by step.

### Step 1: Write down the expressions for A, B, and C.
We have:
- \( A = 3a - 2b \)
- \( B = -2a + 3b \)
- \( C = -a - b \)

### Step 2: Write the expression for \( A + B + C \).
Now, we need to add these three expressions together:
\[ A + B + C = (3a - 2b) + (-2a + 3b) + (-a - b) \]

### Step 3: Combine like terms.
Let's combine the terms with \( a \) and the terms with \( b \):
- For the \( a \) terms: \( 3a - 2a - a \)
- For the \( b \) terms: \( -2b + 3b - b \)

Calculating the \( a \) terms:
\[ 3a - 2a - a = (3 - 2 - 1)a = 0a = 0 \]

Calculating the \( b \) terms:
\[ -2b + 3b - b = (-2 + 3 - 1)b = 0b = 0 \]

### Step 4: Write the final result.
Now, putting it all together:
\[ A + B + C = 0 + 0 = 0 \]

Thus, the final answer is:
\[ \boxed{0} \]

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