Question

Multiply the polynomial expression (x+2)(x−4)%0D%0A(%0D%0A𝑥%0D%0A+%0D%0A2%0D%0A)%0D%0A(%0D%0A𝑥%0D%0A−%0D%0A4%0D%0A)%0D%0A .(2 points)%0D%0Ax2+%0D%0A𝑥%0D%0A2%0D%0A+%0D%0Ax+%0D%0A𝑥%0D%0A+

Answer 1

To multiply the polynomial expressions \((x + 2)(x - 4)\), we can use the distributive property (also known as the FOIL method for binomials).

**Step 1: Apply the FOIL Method**

1. **F (First):** Multiply the first terms:
\[
x \cdot x = x^2
\]

2. **O (Outer):** Multiply the outer terms:
\[
x \cdot (-4) = -4x
\]

3. **I (Inner):** Multiply the inner terms:
\[
2 \cdot x = 2x
\]

4. **L (Last):** Multiply the last terms:
\[
2 \cdot (-4) = -8
\]

**Step 2: Combine Like Terms**

Now we add all of these results together:
\[
x^2 - 4x + 2x - 8
\]

Combine the like terms (\(-4x + 2x\)):
\[
x^2 - 2x - 8
\]

**Final Result:**
Thus, the product of the expression \((x + 2)(x - 4)\) is
\[
\boxed{x^2 - 2x - 8}
\]