## Simplifying the Expression (-x - 8)(x - 8) + x(x + 16)

This article will guide you through the process of simplifying the algebraic expression: **(-x - 8)(x - 8) + x(x + 16)**. We will utilize the distributive property and combine like terms to arrive at a simplified form.

### Step 1: Expand the Products

We begin by expanding the products using the distributive property. Remember that multiplying a sum by a term means multiplying each term inside the sum by that term:

**(-x - 8)(x - 8):**- -x(x - 8) - 8(x - 8) = -x² + 8x - 8x + 64 = -x² + 64

**x(x + 16):**- x² + 16x

### Step 2: Combine Like Terms

Now we have the expanded expression: **-x² + 64 + x² + 16x**

Notice that we have both -x² and +x². These are like terms and cancel each other out. Similarly, we have 16x.

### Step 3: Simplified Expression

Combining the remaining terms, we obtain the simplified expression: **16x + 64**.

### Conclusion

Therefore, the simplified form of the expression **(-x - 8)(x - 8) + x(x + 16)** is **16x + 64**.