Multiply the polynomial expression (x+2)(x−4).(2 points)

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1 answer

To multiply the polynomial expressions \((x + 2)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials).

\[ (x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) \]

Now, let's calculate each term:

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

Now, combine all the terms:

\[ x^2 - 4x + 2x - 8 \]

Combine the like terms \(-4x\) and \(2x\):

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

So, the result of the multiplication is:

\[ \boxed{x^2 - 2x - 8} \]