Question

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

\[
\boxed{x^2 + 6x - 16}
\]