Question

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

Answer 1

To rewrite the polynomial \((x+8)(x-2)\) using the Distributive Property (also known as the FOIL method for binomials), we will distribute each term in the first parentheses to each term in the second parentheses:

1. First: \(x \cdot x = x^2\)
2. Outer: \(x \cdot (-2) = -2x\)
3. Inner: \(8 \cdot x = 8x\)
4. Last: \(8 \cdot (-2) = -16\)

Now, combine all these results:

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

Next, combine the like terms \(-2x\) and \(8x\):

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

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

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