To multiply the polynomial expressions \((x + 2)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials). Here’s how it works step-by-step:
-
Multiply the first terms:
\(x \cdot x = x^2\) -
Multiply the outer terms:
\(x \cdot (-4) = -4x\) -
Multiply the inner terms:
\(2 \cdot x = 2x\) -
Multiply the last terms:
\(2 \cdot (-4) = -8\)
Now, combine all these results together:
\[ x^2 - 4x + 2x - 8 \]
Next, combine like terms:
\[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]
So, the product of the polynomial expression \((x + 2)(x - 4)\) is:
\[ \boxed{x^2 - 2x - 8} \]
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