(x-8)%2Bx(x%2B16).jpeg "(-x-8)(x-8)+x(x+16)")
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.