Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2)%0D%0A(%0D%0A𝑥%0D%0A+%0D%0A8%0D%0A)%0D%0A(%0D%0A𝑥%0D%0A−%0D%0A2%0D%0A)%0D%0A .

Answer 1

write the equation

Answer 2

To rewrite the polynomial \((x+8)(x−2)\) using the Distributive Property, we'll distribute each term in the first binomial by each term in the second binomial.

1. Start with the expression:
\[
(x + 8)(x - 2)
\]

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

3. Next, distribute \(8\) to both terms in the second binomial \((x - 2)\):
\[
8 \cdot (x) + 8 \cdot (-2) = 8x - 16
\]

4. Now combine all the distributed terms:
\[
x^2 - 2x + 8x - 16
\]

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

Thus, the expression \((x + 8)(x - 2)\) can be rewritten using the Distributive Property as:
\[
x^2 + 6x - 16
\]

Answer 3

The equation from the polynomial obtained by using the Distributive Property for \((x + 8)(x - 2)\) is:

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

This represents the polynomial equation after expanding the product. If you want to set it equal to something (like 0 for finding roots), you could write:

\[
x^2 + 6x - 16 = 0
\]

Let me know if you need further assistance!