Find the following products.
`(a+1)(a-1)(a^(2)+1)`

Answer

To find the product \((a+1)(a-1)(a^2+1)\), we can follow these steps:

### Step 1: Use the Difference of Squares
First, we can simplify \((a+1)(a-1)\) using the difference of squares formula, which states that \(x^2 - y^2 = (x+y)(x-y)\). Here, we can let \(x = a\) and \(y = 1\).

\[ (a+1)(a-1) = a^2 - 1 \]

### Step 2: Substitute Back into the Expression
Now, we can substitute \(a^2 - 1\) back into the original expression:

\[ (a^2 - 1)(a^2 + 1) \]

### Step 3: Use the Difference of Squares Again
Next, we can again apply the difference of squares formula to \((a^2 - 1)(a^2 + 1)\). Here, let \(x = a^2\) and \(y = 1\):

\[ (a^2 - 1)(a^2 + 1) = a^4 - 1 \]

### Final Answer
Thus, the product \((a+1)(a-1)(a^2+1)\) simplifies to:

\[ \boxed{a^4 - 1} \]

---