Use distributive property to rewrite the polynomial (x+8)(x-2).

Question

□x²+□x+□

Answer 1

To rewrite the polynomial $(x+8)(x-2)$ using the distributive property, we can apply the FOIL method (First, Outside, Inside, Last).

Let's break this down:

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

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

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

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

Now, combine all these results together:

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

Now, combine the like terms $-2x+8x$:

$$x^2+(8-2)x-16=x^2+6x-16$$

So the polynomial $(x+8)(x-2)$ can be rewritten as:

$$\boxed{{\displaystyle x^2+6x-16}}$$