Question

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

Answer 1

To rewrite the polynomial \((x + 8)(x - 2)\) using the Distributive Property, we need to distribute each term in the first parentheses by each term in the second parentheses.

Here's how it's done step by step:

1. Distribute \(x\) to both terms in the second parentheses:
\[
x \cdot (x - 2) = x^2 - 2x
\]

2. Distribute \(8\) to both terms in the second parentheses:
\[
8 \cdot (x - 2) = 8x - 16
\]

3. Now, combine all the terms from steps 1 and 2:
\[
x^2 - 2x + 8x - 16
\]

4. Combine the like terms \(-2x\) and \(8x\):
\[
x^2 + 6x - 16
\]

So, the polynomial \((x + 8)(x - 2)\) can be rewritten as:
\[
\boxed{x^2 + 6x - 16}
\]