Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2) .(2 points) __x^2 + __x + __

Answer 1

To use the Distributive Property to rewrite the polynomial \((x+8)(x-2)\), we'll apply the distributive property (also known as the FOIL method for binomials).

1. **First:** Multiply the first terms: \(x \cdot x = x^2\).
2. **Outer:** Multiply the outer terms: \(x \cdot (-2) = -2x\).
3. **Inner:** Multiply the inner terms: \(8 \cdot x = 8x\).
4. **Last:** Multiply the last terms: \(8 \cdot (-2) = -16\).

Now, combine these results:

\[
x^2 - 2x + 8x - 16 = x^2 + (8x - 2x) - 16 = x^2 + 6x - 16
\]

Thus, the polynomial rewritten using the Distributive Property is:

\[
x^2 + 6x - 16
\]

In the format requested, the answer is:
- __x^2 + __x + __
- \(1\) (for \(x^2\)), \(6\) (for \(x\)), \(-16\) (the constant term).

So the final answer is:
\(1, 6, -16\)