Subtract the sum of `a+2b-3c and 2c-3b-4a` from the sum of `5b-4c+a and 2c-3b-4a`.

Answer

To solve the problem, we need to follow these steps:

**Step 1: Identify the expressions to be summed.**
We have two pairs of expressions:
1. The first pair: \(5b - 4c + a\) and \(2c - 3b - 4a\)
2. The second pair: \(a + 2b - 3c\) and \(2c - 3b - 4a\)

**Step 2: Calculate the sum of the first pair.**
Let's add the first pair:
\[ (5b - 4c + a) + (2c - 3b - 4a) \]
Combine like terms:
- For \(b\): \(5b - 3b = 2b\)
- For \(c\): \(-4c + 2c = -2c\)
- For \(a\): \(a - 4a = -3a\)

So, the sum of the first pair is:
\[ 2b - 2c - 3a \]

**Step 3: Calculate the sum of the second pair.**
Now, let's add the second pair:
\[ (a + 2b - 3c) + (2c - 3b - 4a) \]
Combine like terms:
- For \(b\): \(2b - 3b = -b\)
- For \(c\): \(-3c + 2c = -c\)
- For \(a\): \(a - 4a = -3a\)

So, the sum of the second pair is:
\[ -3a - b - c \]

**Step 4: Subtract the sum of the second pair from the sum of the first pair.**
Now we need to subtract the second sum from the first:
\[ (2b - 2c - 3a) - (-3a - b - c) \]
This is equivalent to:
\[ 2b - 2c - 3a + 3a + b + c \]
Combine like terms:
- For \(b\): \(2b + b = 3b\)
- For \(c\): \(-2c + c = -c\)
- The \(a\) terms cancel out: \(-3a + 3a = 0\)

So, the final result is:
\[ 3b - c \]

**Final Answer:**
The result of the subtraction is \(3b - c\).

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