Multiply by using the correct identity
`(x+y-z)(x^(2)+y^(2)+z^(2)-xy+xz+yz)`

Answer

To solve the problem `(x+y-z)(x^2+y^2+z^2-xy+xz+yz)` using the correct identity, we will follow these steps:

### Step 1: Identify the Identity
We recognize that the expression can be simplified using the identity:
\[ a + b + c = a + b + c \]
\[ a^2 + b^2 + c^2 - ab - ac - bc = a^3 + b^3 + c^3 - 3abc \]
In our case, we can let:
- \( a = x \)
- \( b = y \)
- \( c = -z \)

### Step 2: Substitute into the Identity
Now we substitute \( a \), \( b \), and \( c \) into the identity:
\[ (x + y - z)(x^2 + y^2 + z^2 - xy + xz + yz) \]

### Step 3: Apply the Identity
According to the identity, we can rewrite the expression as:
\[ x^3 + y^3 + (-z)^3 - 3xy(-z) \]
This simplifies to:
\[ x^3 + y^3 - z^3 + 3xyz \]

### Step 4: Write the Final Answer
Thus, the final result of multiplying the two expressions is:
\[ x^3 + y^3 - z^3 + 3xyz \]

---