What should be subtracted from `x+2y-3z` to get `3x-2y +z`?

Answer

To find out what should be subtracted from the expression \(x + 2y - 3z\) to get \(3x - 2y + z\), we can set up the equation as follows:

1. **Set up the equation**:
Let \(a\) be the expression we need to find. We can write the equation:
\[ (x + 2y - 3z) - a = (3x - 2y + z) \]

2. **Rearrange the equation**:
To isolate \(a\), we can rearrange the equation:
\[ a = (x + 2y - 3z) - (3x - 2y + z) \]

3. **Distribute the negative sign**:
Now, we will distribute the negative sign across the second expression:
\[ a = x + 2y - 3z - 3x + 2y - z \]

4. **Combine like terms**:
Now, we will combine the like terms:
- For \(x\): \(x - 3x = -2x\)
- For \(y\): \(2y + 2y = 4y\)
- For \(z\): \(-3z - z = -4z\)

Putting it all together, we get:
\[ a = -2x + 4y - 4z \]

5. **Conclusion**:
Therefore, the expression that should be subtracted from \(x + 2y - 3z\) to obtain \(3x - 2y + z\) is:
\[ -2x + 4y - 4z \]