Add `x^2yz,2yzx^2 and -4zx^2y`

Answer

To add the algebraic expressions \(x^2yz\), \(2yzx^2\), and \(-4zx^2y\), we follow these steps:

### Step 1: Identify Like Terms
The expressions we have are:
1. \(x^2yz\)
2. \(2yzx^2\)
3. \(-4zx^2y\)

All three terms are like terms because they contain the same variables raised to the same powers:
- \(x^2\) (power of 2)
- \(y\) (power of 1)
- \(z\) (power of 1)

### Step 2: Rewrite the Terms
We can rewrite \(2yzx^2\) in a more standard form:
- \(2yzx^2 = 2x^2yz\)

Now we have:
1. \(x^2yz\)
2. \(2x^2yz\)
3. \(-4x^2yz\)

### Step 3: Combine the Coefficients
Next, we add the coefficients of the like terms:
- The coefficient of \(x^2yz\) is \(1\).
- The coefficient of \(2x^2yz\) is \(2\).
- The coefficient of \(-4x^2yz\) is \(-4\).

Now we calculate:
\[ 1 + 2 - 4 = -1 \]

### Step 4: Write the Final Expression
Now we combine the result with the common variable part:
\[ -1 \cdot x^2yz = -x^2yz \]

Thus, the final answer is:
\[ -x^2yz \]