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:
-
First: Multiply the first terms:
\(x \cdot x = x^2\) -
Outside: Multiply the outer terms:
\(x \cdot (-2) = -2x\) -
Inside: Multiply the inner terms:
\(8 \cdot x = 8x\) -
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:
\[ \boxed{x^2 + 6x - 16} \]