Use the Distributive Property to rewrite the polynomial (x+8)(x−2)

.(2 points)
__x^2+ __x+___

1 answer

To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we'll distribute each term in the first parenthesis to each term in the second parenthesis.

  1. Distribute \(x\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]

  2. Distribute \(8\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]

  3. Now, combine all the terms: \[ x^2 - 2x + 8x - 16 \] Combine the like terms \(-2x\) and \(8x\): \[ x^2 + 6x - 16 \]

So, the polynomial \((x + 8)(x - 2)\) can be rewritten as: \[ \boxed{x^2 + 6x - 16} \] where \(1\) is the coefficient of \(x^2\), \(6\) is the coefficient of \(x\), and \(-16\) is the constant term.