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multiply the polynomial expression (x+2)(x-4)

__x^2+__x+__

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To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (FOIL method):

  1. First: Multiply the first terms:
    \(x \cdot x = x^2\)

  2. Outside: Multiply the outside terms:
    \(x \cdot (-4) = -4x\)

  3. Inside: Multiply the inside terms:
    \(2 \cdot x = 2x\)

  4. Last: Multiply the last terms:
    \(2 \cdot (-4) = -8\)

Now, combine all these results:
\[ x^2 - 4x + 2x - 8 \]

Combine like terms:
\[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]

Thus, the expanded polynomial expression is:
\[ x^2 - 2x - 8 \]

So the answer is:
x^2 + (-2)x + (-8).