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:

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