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

Question

x^2+ x+

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials), we multiply each term in the first binomial by each term in the second binomial.

Given the polynomial $(x+8)(x-2)$:

1. First: Multiply the first terms:
   $x\cdot x=x^2$

2. Outer: Multiply the outer terms:
   $x\cdot (-2)=-2x$

3. Inner: Multiply the inner terms:
   $8\cdot x=8x$

4. Last: Multiply the last terms:
   $8\cdot (-2)=-16$

Now, combine all these results:

$$x^2-2x+8x-16$$

Combine the like terms $-2x$ and $8x$:

$$x^2+6x-16$$

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

$$x^2+6x-16$$