Question

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

x2+ x+

Answer 1

To use the Distributive Property to rewrite the polynomial \((x+8)(x−2)\), we can distribute each term in the first polynomial by each term in the second polynomial.

1. Distribute \(x\) across \((x - 2)\):
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distribute \(8\) across \((x - 2)\):
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

3. Now, combine all the terms together:
\[
x^2 - 2x + 8x - 16
\]

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

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