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 (also known as the FOIL method for binomials), we multiply each term in the first binomial by each term in the second binomial.

Given the polynomial \((x + 8)(x - 2)\):

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 all these results:

\[
x^2 - 2x + 8x - 16
\]

Combine the like terms \(-2x\) and \(8x\):

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

Thus, the polynomial \((x + 8)(x - 2)\) rewritten using the Distributive Property is:

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