Find each of the following products :
`(x^(2) - xy + y^(2)) xx (x + y)`

Answer

To find the product of the expressions \( (x^2 - xy + y^2) \) and \( (x + y) \), we can follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ (x^2 - xy + y^2)(x + y) \]

### Step 2: Distribute the first term
We will first multiply \( x^2 \) by each term in \( (x + y) \):
\[ x^2 \cdot x + x^2 \cdot y = x^3 + x^2y \]

### Step 3: Distribute the second term
Next, we multiply \( -xy \) by each term in \( (x + y) \):
\[ -xy \cdot x + (-xy) \cdot y = -x^2y - y^2x \]

### Step 4: Distribute the third term
Now, we multiply \( y^2 \) by each term in \( (x + y) \):
\[ y^2 \cdot x + y^2 \cdot y = y^2x + y^3 \]

### Step 5: Combine all the results
Now we combine all the results from the previous steps:
\[ x^3 + x^2y - x^2y - y^2x + y^2x + y^3 \]

### Step 6: Simplify the expression
Notice that \( x^2y \) and \( -x^2y \) cancel each other out, as do \( -y^2x \) and \( y^2x \):
\[ x^3 + y^3 \]

### Final Result
Thus, the product of the two expressions is:
\[ x^3 + y^3 \]

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