To multiply the polynomial expressions \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials).
Here's how it works step by step:
-
First: Multiply the first terms:
\(x \cdot x = x^2\) -
Outer: Multiply the outer terms:
\(x \cdot (-4) = -4x\) -
Inner: Multiply the inner terms:
\(2 \cdot x = 2x\) -
Last: Multiply the last terms:
\(2 \cdot (-4) = -8\)
Now, combine all these results: \[ x^2 - 4x + 2x - 8 \]
Combine like terms: \[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]
So the final result is: \[ x^2 - 2x - 8 \]
Thus, to complete your expression, it should be: \(x^2 - 2x - 8\)