To multiply the polynomial expressions \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials), where we multiply each term in the first binomial by each term in the second binomial.
Here’s the step-by-step multiplication:
-
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 together: \[ x^2 - 4x + 2x - 8 \]
Next, combine like terms \(-4x + 2x\): \[ x^2 - 2x - 8 \]
Thus, the final result of multiplying the expressions \((x + 2)(x - 4)\) is: \[ \boxed{x^2 - 2x - 8} \]
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