Multiply the polynomial expression (x+2)(x−4).(2 points)

Question

x2+
𝑥
2
+
x+
𝑥
+

Answer 1

To multiply the polynomial expressions \((x + 2)(x - 4)\), you 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 calculate each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-4) = -4x\)
3. \(2 \cdot x = 2x\)
4. \(2 \cdot (-4) = -8\)

Now, combine all the terms:

\[ x^2 - 4x + 2x - 8 \]

Combine the like terms \(-4x\) and \(2x\):

\[ x^2 - 2x - 8 \]

So, the result of the multiplication is:

\[ \boxed{x^2 - 2x - 8} \]