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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**.