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:

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

Now let's perform the multiplication:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-2) = -2x\)
3. \(8 \cdot x = 8x\)
4. \(8 \cdot (-2) = -16\)

Now combine these results:

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

Combine the like terms \(-2x + 8x\):

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

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

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