To multiply the polynomial expression \((x + 2)(x - 4)\), you 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. Next, multiply the outer terms:
\[
x \cdot (-4) = -4x
\]
3. Then, multiply the inner terms:
\[
2 \cdot x = 2x
\]
4. Finally, multiply the last terms:
\[
2 \cdot (-4) = -8
\]
Now, combine all these results:
\[
x^2 - 4x + 2x - 8
\]
Combine the like terms (\(-4x + 2x\)):
\[
x^2 - 2x - 8
\]
So the final answer is:
\[
x^2 - 2x - 8
\]
In the format you requested, it would be:
- \(1\) for the coefficient of \(x^2\),
- \(-2\) for the coefficient of \(x\),
- \(-8\) for the constant term.
Thus, the answer is:
\[
(x^2 + (-2)x + (-8))
\]