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

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1 answer

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:

\[ (x + 8)(x - 2) = x \cdot x + x \cdot (-2) + 8 \cdot x + 8 \cdot (-2) \]

Now let's perform the multiplication:

  1. \(x \cdot x = x^2\)
  2. \(x \cdot (-2) = -2x\)
  3. \(8 \cdot x = 8x\)
  4. \(8 \cdot (-2) = -16\)

Now combine these results:

\[ x^2 - 2x + 8x - 16 \]

Combine the like terms \(-2x + 8x\):

\[ x^2 + 6x - 16 \]

Thus, the polynomial \((x + 8)(x - 2)\) is rewritten as:

\[ x^2 + 6x - 16 \]