Question

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

Answer 1

To apply the Distributive Property to the expression \((x + 8)(x - 2)\), we multiply each term in the first parentheses by each term in the second parentheses:

\[
(x + 8)(x - 2) = x(x - 2) + 8(x - 2)
\]

Now, we distribute:

1. \(x(x - 2) = x^2 - 2x\)
2. \(8(x - 2) = 8x - 16\)

Now, we combine the results:

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

Combining like terms \(-2x + 8x\):

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

Thus, the polynomial \((x + 8)(x - 2)\) can be rewritten as:

\[
\boxed{x^2 + 6x - 16}
\]