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:

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