To multiply \( (x - 4)(x + 2) \), we can apply the distributive property (also known as the FOIL method for binomials):
\[ (x - 4)(x + 2) = x \cdot x + x \cdot 2 - 4 \cdot x - 4 \cdot 2 \]
Calculating each term:
- \( x \cdot x = x^2 \)
- \( x \cdot 2 = 2x \)
- \( -4 \cdot x = -4x \)
- \( -4 \cdot 2 = -8 \)
Now, combine the terms:
\[ x^2 + 2x - 4x - 8 = x^2 - 2x - 8 \]
So, the final result is:
\[ x^2 - 2x - 8 \]
The correct response from your options is:
\(x^2 - 2x - 8\).