To use the Distributive Property to rewrite the polynomial \((x+8)(x−2)\), we can distribute each term in the first polynomial by each term in the second polynomial.
-
Distribute \(x\) across \((x - 2)\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]
-
Distribute \(8\) across \((x - 2)\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]
-
Now, combine all the terms together: \[ x^2 - 2x + 8x - 16 \]
-
Combine like terms: \[ x^2 + (8x - 2x) - 16 = x^2 + 6x - 16 \]
So the polynomial \((x+8)(x−2)\) can be rewritten as: \[ x^2 + 6x - 16 \]