Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2) .(2 points) x2+x+

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we multiply each term in the first binomial by each term in the second binomial.

1. First, multiply the first terms:
\[
x \cdot x = x^2
\]

2. Next, multiply the outer terms:
\[
x \cdot (-2) = -2x
\]

3. Then, multiply the inner terms:
\[
8 \cdot x = 8x
\]

4. Finally, multiply the last terms:
\[
8 \cdot (-2) = -16
\]

Now, combine all these results:
\[
x^2 - 2x + 8x - 16
\]

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

So the polynomial \((x + 8)(x - 2)\) expanded using the Distributive Property is:
\[
x^2 + 6x - 16
\]