Find each of the following products :
`(x^(4) + y^(4)) xx (x^(2) - y^(2))`

Answer

To solve the expression \((x^{4} + y^{4}) \cdot (x^{2} - y^{2})\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step breakdown of the solution:

### Step 1: Distribute the first term of the first expression
We start by distributing \(x^{4}\) to both terms in the second expression \((x^{2} - y^{2})\).

\[ x^{4} \cdot (x^{2} - y^{2}) = x^{4} \cdot x^{2} - x^{4} \cdot y^{2} \]

### Step 2: Simplify the first distribution
Now we simplify each term:

1. \(x^{4} \cdot x^{2} = x^{4 + 2} = x^{6}\)
2. \(-x^{4} \cdot y^{2} = -x^{4}y^{2}\)

So, from Step 1, we have:

\[ x^{6} - x^{4}y^{2} \]

### Step 3: Distribute the second term of the first expression
Next, we distribute \(y^{4}\) to both terms in the second expression \((x^{2} - y^{2})\).

\[ y^{4} \cdot (x^{2} - y^{2}) = y^{4} \cdot x^{2} - y^{4} \cdot y^{2} \]

### Step 4: Simplify the second distribution
Now we simplify each term:

1. \(y^{4} \cdot x^{2} = y^{4}x^{2}\)
2. \(-y^{4} \cdot y^{2} = -y^{4 + 2} = -y^{6}\)

So, from Step 3, we have:

\[ y^{4}x^{2} - y^{6} \]

### Step 5: Combine all the terms
Now we combine all the results from Steps 2 and 4:

\[ x^{6} - x^{4}y^{2} + y^{4}x^{2} - y^{6} \]

### Final Result
Thus, the final expression is:

\[ x^{6} - x^{4}y^{2} + y^{4}x^{2} - y^{6} \]