Multiply the polynomial expression (x + 2) (x - 4).

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

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

2. **Outer:** Multiply the outer terms:
\(x \cdot (-4) = -4x\)

3. **Inner:** Multiply the inner terms:
\(2 \cdot x = 2x\)

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

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

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

So, the final result is:
\[
x^2 - 2x - 8
\]

Thus, filling in the blanks:
__x^2 + _x + _
The completed expression is:
**x^2 - 2x - 8**.