To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials):
\[ (x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) \]
Now, let's break it down step by step:
- \(x \cdot x = x^2\)
- \(x \cdot (-4) = -4x\)
- \(2 \cdot x = 2x\)
- \(2 \cdot (-4) = -8\)
Now, combine all these results:
\[ x^2 - 4x + 2x - 8 \]
Combine like terms:
\[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]
Thus, the final result of multiplying \((x + 2)(x - 4)\) is:
\[ x^2 - 2x - 8 \]
So, filling in the blanks:
- \(x^2 +\)
- \(-2x +\)
- \(-8\)
The complete answer is:
\[ x^2 - 2x - 8 \]